Items tagged with summation

Hello everybody,

I am trying to solve the following integral which also has summation but it gives me strange results. Do anyone know if I am doing something wrong?

The equation is in black and the strange result is in blue.

Thank you !

Dear All

Please see my query below:


Suppose I have a expression whose terms are in summation:

sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity)

sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity)


diff(sum(P[n]*xi^n, n = 0 .. infinity)+(sum(P[n]*xi^n, n = 0 .. infinity))^2+sum(P[2*n+1]*P[2*n]*xi^n, n = 0 .. infinity), xi)

sum(P[n]*xi^n*n/xi, n = 0 .. infinity)+2*(sum(P[n]*xi^n, n = 0 .. infinity))*(sum(P[n]*xi^n*n/xi, n = 0 .. infinity))+sum(P[2*n+1]*P[2*n]*xi^n*n/xi, n = 0 .. infinity)


In above summation, how I can write specific term ? For example, how I can display term for n = 2etc.




Consider the expression infinityn=1 (-1)n ebeta*n/n2


1. Find the symbolic value of this sum.

2. Find an approximation for the value when beta= -2.

3. Build a function to calculate an approximation for the value of the given expression for

any value for beta


Hi, so I have few problems here. I need to;

Create a MxN Matrix/Lattice, where N and M can be any positive integer, that contains a random selection of -1/1s at each entry.

Need to sum every entry, then multiply by -1 to find “H”.

Need to multiply each neighbour to find its bond energy, so if it’s the same you get 1 else -1, but only its direct neighbours once, so if it was a 2x2 matrix there would be only 4 values and then sum them.

I don’t seem to be able to set up the code so that it does it for any size matrix, as I only know how to write it out basic for a 2x2. Also, not so important, but I wanted to know if could create a loop that would find every iteration of possible setups i.e. for a 2x1 you can have 1.1, -1.1, 1.-1, -1.-1. And then give the solutions outlined earlier for each of the the possibilities [There being 2MxN ]

Cheers in advance.

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:


But the result I get:



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


Thank you.


I have encountered some strange issue with symbolic summation. Would be grateful for any help.

Here is the code (inserted as image):

Symbolic summation of powers of sines & cosines


Code in text:



The issue is that symbolic summation produces the formula (for general n) which contradicts the particular case (n=4).

Could somebody explain why this is happening? Is it a bug or am I missing something here?

I have tried all versions of Maple downto 14 - same situation.
Also Mathematica givers the same answer.

Thank you in advance,
Pavel Holoborodko.

Multiprecision Computing Toolbox

Hello people in mapleprimes,

I want to distribute limit or Limit to each terms of summation.


But, the output is not distributed one, but the same as the input, though

I want it to become Limit(f(a+h),h=0)+Limit(f(a),h=0), or


Isn't there any way for it, other than a trivial one that is



I hope someone will teach me.

Thanks in advance.




Any idea about the summation of Fibonacci sequence


Best regards


How can Maple solve that problem for me?

Given: a summation of one equation with its limits, equaling another summation with given limits, but NOt the equation. How do Maple be programmed to find that out? 


fx     [sum(x^(n)*y^(1-n), n=0..10, = sum(unknownequation),n=1..11)]   , find the unknown equation by maple?


Appreciating in advance,

How do I multiply the 4x into the summation to get  (Sum(4*n*a[n]*x^(n), n = 0 .. infinity))  and same idea for the 3rd third?

Also, how do I go from   Sum(a[n-2]*x^(n-2), n = 2 .. infinity)  to  Sum(a[n]*x^(n), n = 0 .. infinity)  by manipulating the indices?


I have the following expression.


What I want to do is take the derivative of this expression with respect to,


Where L is somewhere between 1 and n. 

Using the diff operator, I would like to get something like,


But I don't.  Instead, I get zero.  I want to leave n undefined so that the summation isn't automatically expanded out to alot of terms, thereby making it much more difficult to read.  This is especially true as my formulas become more complicated.




Find S=1+1/2+1/3+1/4+...+1/n ,n is integers .

I'm trying to solve a system of equations thats expressed as a summation (the original has the summation symbol as opposed to 'sum'):

d_actual := solve(W_actual = sum(W_guess(def-asp_rad_inverse[i], E, asp_rad[i]), i = 1 .. n), def);

When n<5, I get an answer after a few seconds, but when n is higher, the program sits and 'evaluates' forever...I've waited up to 30 min. 


I have a plate with a number of hemispheres on the surface (# of impacted hemispheres given a force = n). Each has a unique radius and they're listed from largest to smallest in 'asp_rad[]'. I have an equation for the deflection of a single hemisphere as a function of Force and material properties that I have rearranged with respect to Force (W_guess(deflection, E, r)). There's an opposing plate that stays parallel to the original plate while pushing down on the asperities with Force W_actual. The total deflection of the opposing plate is the sum of: 1) the difference between the tallest radius and the impacted radius in question (asp_rad_inverse[]), and 2) the deflection of the impacted radius in question. 

I'm attempting to solve for the total deflection of the opposing plate via solving for the 'def' in the summation above, but when I run it, the program is not able to compute a solution.

Thanks in advance.

How can I solve the following system in Maple for $S_1$ and $S_{i+1}$? I have the code written, but it is giving me nothing as output.

eq1 := Q-A*S[1]*C/X+B*D*(sum(S[j], j = 2 .. i+1))/Y-r[1]*S[1] = 0;
eq2 := A*S[i-1]*C/X-A*S[i]*C/X-B*S[i]*D/Y-r[1]*S[i] = 0;
eq3 := A*S[i]*C/X-B*S[i+1]*D/(Y+S[i+1])-r[2]*S[i+1] = 0;
solve({eq1, eq2, eq3}, {S[1], S[i+1]});

The only non-constants in the system are the $S_j$'s for $j = 1, \ldots, i+1$.

Here is the system in math mode:
$$Q-\frac{AC}{X}S_1-r_1 S_1 +\frac{BD}{Y}\sum\limits_{j=2}^{i+1}S_j = 0 \\
\frac{AC}{X}S_{i-1} - \frac{AC}{X}S_i - \frac{BD}{Y}S_i - r_1 S_i = 0\\
\frac{AC}{X}S_i - \frac{BD S_{i+1}}{Y+S_{i+1}} - r_2 S_{i+1} = 0 $$

I have a head start on it by hand, but it's too cumbersome to complete.

Basically, my strategy is to solve for $S_{i+1}$ as a function of $S_1$ and some constants. Then to plug in $S_2, \ldots, S_{i+1}$ in the summation and solve for $S_1$ as a function of constants. Then I would obtain $S_{i+1}$ as a function of constants itself.

Thanks for any help.



I have a problem with creating a function contains n-dimensional independent variables with random function .. The function looks like:

f(x)=sum(U[i] * abs(x[i])^i,i=1..n)

where U is a random between 0 and 1


For 1-dimensional problem, it will be like:


The plot by MATLAB will be:


While, for 2-dimensional problem, it will be like:

f(x[1],x[2])=U[1]*abs(x[1]) - (-U[2]*abs(x[2])^2)


and the plot with MATLAB will be:


The MATLAB code is:

R=1000; % steps resolution

for j=1:length(x1)

    % For 1-dimensional plotting

    % For 2-dimensional plotting
    for i=1:length(x2)







I have used Maple because of its great graphics and animation, and for the mathematical analysis capability. However, to animate the above problem for 1- and 2-dimensional problems, I always fail!

My attempt has been just successed to plot 1-dimensional problem (without animation) .. And it tooks long-time with many codes!


X := Statistics:-RandomVariable(('Uniform')(0, 1));
R := Statistics:-Sample(X, 1000);

Vect := abs(Vector[column]([seq(0 .. 10, 10/999)]));

V := `~`[`-`](Vect, 5);

Mat := Multiply(V, R);

f := ArrayTools:-Diagonal(Mat);

F := abs(f);

Axis := Transpose(V);

f5 := plot(Axis, F, style = line);


And finally I got the graph:


But the problem is:

How can I animate it? Maybe I need to express it with new Maple code?

How can I plot and animate it when n=2?



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