Items tagged with sum

I am having issues with Maple 2016 computing closed form solutions using the sum command. For example, sum((-1)^n, n = 1 .. infinity) evaluates to -1/2 in the help topic, however, when I run the command in a maple document, this result is not obtained. It instead returns sum((-1)^n, n = 1 .. infinity). Likewise, sum( a*r^k, k = 0..infinity) doesn't evaluate to -a/(r-1). How can I get Maple to determine closed form solutions for power series?

i wrote this problem to solve 

Delta= Sum(j=1 to n)SUM(i=j to n)(pi*hj/Ad(t,ij)*Et,ij))

Where n=70,  G= ftj (t)/(4+0.85*t) , where (t =8, 16, 24,…….up to 8*n), hj= 13 for all j except j1 =18

Ad= (Aj+s(mij-1)), where Aj varies

Mij=ES/E(G),          where E(G)= 57sqrt(1000*G)

 

n := 70;

70

(1)

i := seq(1 .. n, 1);

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

(2)

t := proc (i) options operator, arrow; 8*i end proc;

proc (i) options operator, arrow; 8*i end proc

(3)

j := i;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

(4)

F = f(j);

F = f(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70)

(5)

F(1 .. 30) := 8;

8

(6)

F(31 .. 40) := 7;

7

(7)

F(41 .. 70) := 6;

6

(8)

G := proc (F, i) options operator, arrow; F*t/(4+.85*t) end proc;

proc (F, i) options operator, arrow; F*t/(4+.85*t) end proc

(9)

A := f(j);

f(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70)

(10)

A(1 .. 30) := 5184;

5184

(11)

A(31 .. 50) := 3600;

3600

(12)

A(51 .. 62) := 1936;

1936

(13)

A(63 .. 70) := 1024;

1024

(14)

s := f(j);

proc () option remember; table( [( 31 .. 50 ) = 3600, ( 63 .. 70 ) = 1024, ( 1 .. 30 ) = 5184, ( 51 .. 62 ) = 1936, ( 31 .. 40 ) = 3600 ] ) 'procname(args)' end proc

(15)

s(1 .. 10) := 128.0448;

128.0448

(16)

s(11 .. 20) := 63.763;

63.763

(17)

s(21 .. 30) := 79.92;

79.92

(18)

s(31 .. 40) := 64.08;

64.08

(19)

s(41 .. 50) := 47.88:

s(51 .. 62) := 31.944;

31.944

(20)

s(63 .. 70) := 12.49;

12.49

(21)

E := proc (G) options operator, arrow; 57*sqrt(1000*F) end proc;

proc (G) options operator, arrow; 57*sqrt(1000*F) end proc

(22)

Es := 29000;

29000

(23)

m := proc (E) options operator, arrow; Es/E(G) end proc;

proc (E) options operator, arrow; Es/E(G) end proc

(24)

Ad := proc (j, m) options operator, arrow; A+s*(m(E)-1) end proc;

proc (j, m) options operator, arrow; A+s*(m(E)-1) end proc

(25)

P := f(j);

proc () option remember; table( [( 21 .. 30 ) = 79.92, ( 31 .. 50 ) = 3600, ( 41 .. 50 ) = 47.88, ( 63 .. 70 ) = 12.49, ( 1 .. 30 ) = 5184, ( 51 .. 62 ) = 31.944, ( 11 .. 20 ) = 63.763, ( 31 .. 40 ) = 64.08, ( 1 .. 10 ) = 128.0448 ] ) 'procname(args)' end proc

(26)

P(1 .. 68) := 254.7;

254.7

(27)

P(69 .. 70) := 196.8;

196.8

(28)

h := f(j);

proc () option remember; table( [( 21 .. 30 ) = 79.92, ( 31 .. 50 ) = 3600, ( 41 .. 50 ) = 47.88, ( 63 .. 70 ) = 12.49, ( 1 .. 30 ) = 5184, ( 51 .. 62 ) = 31.944, ( 11 .. 20 ) = 63.763, ( 31 .. 40 ) = 64.08, ( 1 .. 10 ) = 128.0448 ] ) 'procname(args)' end proc

(29)

h(1) := 18;

18

(30)

h(2 .. 70) = 13;

h(2 .. 70) = 13

(31)

delta := sum(sum((P.h)/(E(G)*Ad)), i = 1 .. n, j = i)

Error, invalid input: sum uses a 2nd argument, k, which is missing

 

``


 

Download short.mw

f=sum((2*q*cos(2* i*x)*(-1)^(i)*(-1)^((2*i-1)))/(i*Pi),i=1.3.5...35)

I want to write this series but getting error

the result is

2*q*cos(2*x)/Pi-2*cos(6*x)*q/(3*Pi)+2*q*cos(10*x)/(5*Pi)-2*q*cos(14*x)/(7*Pi)+2*q*cos(18*x)/(9*Pi)-2*q*cos(22*x)/(11*Pi)+2*q*cos(26*x)/(13*Pi)-2*q*cos(30*x)/(15*Pi)+2*q*cos(34*x)/(17*Pi)-2*q*cos(38*x)/(19*Pi)+2*q*cos(42*x)/(21*Pi)-2*q*cos(46*x)/(23*Pi)+2*q*cos(50*x)/(25*Pi)-2*q*cos(54*x)/(27*Pi)+2*q*cos(58*x)/(29*Pi)-2*q*cos(62*x)/(31*Pi)+2*q*cos(66*x)/(33*Pi)-2*q*cos(70*x)/(35*Pi)

can anybody help 

Hello, I need help in add/sum, there are two problems:

 

1. How we write triple summation (sigma) in Maple? (See pic)

Pic 1 (Triple Sigma)

I try sum(sum(sum or add(add(add but it isn't working.

 

 

2. How we write summation like in this pic?

Pic 2

I already try these syntax:

for e from 1 to 9 do

for k from 1 to 17 do

if i=(2*e-1) then next else

constraint12[2*e-1,k]:=add(x[2*e-1,i,k],i from i in T)=1

end if

end do

end do

 

For example, the expected result for e=2 and k=1 is like following equation:

x[2,1,1]+x[2,3,1]+x[2,4,1]+x[2,5,1]+...+x[2,17,1]+x[2,18,1]=1

But the result I get:

x[2,1,1]+x[2,2,1]+x[2,3,1]+...+x[2,18,1]=1

 

How to omit the x[2,2,1]?

 

Thank you.

Hi! I'm trying to find the way to plot the solution with series representation. I need some help to find the easiest way.

Note: I realized some typing errors, which do not change the question a lot ,and I corrected them.

plot.mw

 

 

 

 

Can we calculate the following equations in Maple?

Substituting equations (21) and (22) into (17), and then obtain equation (23). How to do that? I have done this, but the results are complex and large. They are not in a sum form, but in an expansion form. The reference and the maple file are attached.

Hope for your help.

Best wishes,

Kang

Dynamic_buckling_of_thin_isotropic_plates_subjected_to_in-plane_impact.pdf

gg.mw

Hello,how can i find the lambda in this equation? and x=0..2 , t=0..2

Dear all

 

I have a confusion between these symbol

Sum , add and sum

If we consider u(n) is a sequence and n integer

and what is the difference between 

sum( u(n),n=0..infinity)

Sum(u(n),n=0..infinity)

and sum('u(n)', n=0..infinity)

Many thanks

Hello

Any idea about the summation of Fibonacci sequence

 

Fibonacci.mw

 

Best regards

 

Hello everybody.

I have a function:

f(x,y)=GAMMA(y, -ln(x))/GAMMA(y)

seq(sum(f(x, y), y = 0 .. 1), x = 0 .. 5)

 

and I got a error message:

Error, (in ln) numeric exception: division by zero ??
This is normal behavior in seq function or Bug?

 

but  when I'm first calculate the sum sol := sum(f(x, y), y = 0 .. 1) -> x,

and evalf([seq(sol, x = 0 .. 5)]) ->[0., 1., 2., 3., 4., 5.] works fine.

 

Seq-division_by_zero.mw

Mariusz Iwaniuk

Dear all

 

If its possible in  Maple to change the integral of the sum to  the sum of integrals when I calucle the integral of a function series

 

Thank you

Hello guys,

I was just playing around with the Shanks transformation of a power series, when I noticed that polynomials aren't evaluated as I would expect.
I created this minimal working example; the function s should evaluate for z=0 to a[0], however it return simply 0.
Is there something I messed up?

restart

s := proc (n, z) options operator, arrow; sum(a[k]*z^k, k = 0 .. n) end proc;

proc (n, z) options operator, arrow; sum(a[k]*z^k, k = 0 .. n) end proc

(1)

series(s(n, z), z = 0)

series(a[0]+a[1]*z+a[2]*z^2+a[3]*z^3+a[4]*z^4+a[5]*z^5+O(z^6),z,6)

(2)

The value of s in z=0 should be a[0], however it returns 0:

s(n, 0)

0

(3)

s(1, 0)

0

(4)

Download evaluate_sum.mw

 

Thanks for your help,

Sören

Please check this:

N:=3;

sum1 := lcm(N, 0)+lcm(N, 1)+lcm(N, 2)+lcm(N, 3);

sum2 := sum(lcm(N, k), k = 0 .. N);

 

Why is sum2 wrong?

 

Regards,

César Lozada

 

Hey,

 

I'm trying to make a sum of only odd numbers regarding 2 functions and I've come up with what I assume is a terrible way to do it...

So basically what I want to write is this:

 


And this should give me something like this:


This works, what I have now. The thing is I need to be able to add and subtract terms in order to compare with other stuff and it just seems so inefficient right now.

 

Thanks in advance!

 

 

I have encountered a behavior of Maple that I find hard to explain and I am hoping for help. The command

sum(floor((exp(Pi)-Pi)*n)/3^n,n=0..infinity);

was meant to be an example of "High-precision fraud" as in the 1992 paper of Borwein and Borwein, and indeed it gives 29/2 to within 531 digits. But I am unable to make Maple see this; indeed I get with evalf(%,1000)

14.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

I find it hard to guess why Maple gets this wrong, actually. The point of the example is that floor((exp(Pi)-Pi)*n)=20*n-1 for many n, but Maple has no problems finding the first failure at n=1112. It must hence be trying something more advanced than just adding up all summands until the tail sum is small enough to satisfy the precision? I guess an alternative approach would indeed be possible since what is being "floored" is relatively simple, but then that seems to be buggy?

Would be very grateful for any assistance!

Best,

Soren Eilers

 

 

 

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