## Strange result for sum of binomials...

Dear Maple users,

I recently had to deal with the following sum :

sum(binomial(k+i,k),i=0..infinity)

for an arbitrary positive value of k. This sum obviously seems to diverge but Maple gives me 0 as a result for it. It looks very strange to me, but it might be the same sort of result as the sum of all the positive integers is -1/12. I am wondering whether the result Maple gives me is correct, and if yes, where does it come from ?

Any idea ?

Thanks a lot!

## how do i work with implicit 2-d Plots?...

for example i have this equation: y=x+c , y and x are variable, but c is constant. i want to plot implicitly with respect to y and x, but the result has no line or something and just two axes. what can i do?

## Convert multiple deg to rad and assign each to spe...

If I have 4 latitude and longitude coordinates in degree.  How can I convert all of them to radian and assign each to a specific variable inside a procedure?

>

> DBP(36.9,102.04,37.345,101.6104)
Error, invalid loop statement termination

attached: WA57dev.mw

## or or `or` or Or or OrProp...

```is(k::OrProp(even, odd)) assuming k::integer;
false

is(k::Or(posint, nonposint)) assuming k::integer; # a synonym for OrProp
false

is(`or`(k::posint, k::negint, k = 0)) assuming k::integer;
false
```

Not including the infix or because that would fail for k=0 for different reasons.

## how to solve rational exponent differential equati...

Hey, friends, I have a differential equation to confuse me too much!  The question is shown in the below:

ODEs:

y''(x)-0.00003019*y(x)^0.337=0  ,       0<x<2945

BCs:

y(0)=0,    y'(2945)=0.0116

I want to have the numerical solution, I used to plot y(x) and y'(x) , but errors shows me "jacobian is singular at left endpoint, use midpoint method instead."  Thank you for you any help in advance!!!

Can you give me the code to figure it out in Maple?  Thank you so so so so much!

## Question on eliminate...

1.

```eliminate({-a+x+y+z, -b+x*y+y*z+x*z, -c+x*y*z, -P+x^4+y^4+z^4}, {x, y, z});
[{x = (sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2+a*b*c-c^2)/(2*b*c),
y = -(sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2-a*b*c+c^2)/(2*b*c),
z = c/b}, {-a^4+4*a^2*b-4*a*c-2*b^2+P}],
[{x = -(sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2-a*b*c+c^2)/(2*b*c),
y = (sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2+a*b*c-c^2)/(2*b*c),
z = c/b}, {-a^4+4*a^2*b-4*a*c-2*b^2+P}]
```

The expression for P is fine, but how are x and y square roots and z=c/b??

2.

```eliminate({y*z, x+y-z}, z);
[{z = 0}, {x + y}]
```

Is this supposed to happen? I was expecting y*(x+y):

```Groebner:-Basis({y*z, x+y-z}, lexdeg([z], [x, y]));
[x*y + y^2, z - x - y]
```

## Fit() doesn't fit very well...

I have to fit two lists of data to a function of the type A*sin(bx+c)+d, but when I do (actual data):

X := [seq(i, i = 0 .. 24)];
Y := [1154, 1156, 1156, 1155, 1152, 1143, 1105, 1069, 1051, 1077, 1117, 1154, 1154, 1156, 1158, 1157, 1155, 1152, 1128, 1089, 1058, 1059, 1092, 1130, 1163];

with(Statistics):

f:=Fit(A*sin(b*x+c)+d, X, Y, x);
plot({f(x), [seq([X[i], Y[i]], i = 1 .. 25)]}, x = 0 .. 24, style = [line, point])

They match up very poorly. I can get a better fit by using Geogebra (which produces a function 48.7 * sin(0.52x + 0.56) + 1124.95, which fits the data much better).

I can get a good fit using CurveFitting[Interactive], but the resulting function doesn't fit my target format. What can I do to get a better fit in Maple while staying within the target format?

## recursion in startup code...

Hi, I am currently using the embedded components to make an interface in maple 2016. However, when I executed the startup code, an error was reported, which is 0, "recursive assignment". The recursions are not allowed in the startup code? Anyone can help me with this problem? By the way, how to cancel the warning of executing the startup code when I open the .mw?

Many thanks!

## The smallest time unit which Maple use for reporti...

Is the smallest unit of time that Maple can use to report the computation time millisecond? When I use time(...) the output is a floating-point number with at most three digits after the floating point and since the unit in Maple help is said to be seconds, I'm thinking the smallest time unit it will report is millisecond. Is there any possibility to have more digits in the time reports, let's say up to 10-5 seconds?

## unames() in extended typesetting bug...

unames()   produces an error  in extended typsetting mode (the default in Maple 2017)  after any output.

 > #interface(typesetting=standard);
 > restart;
 > interface(typesetting=extended);
 (1)
 > unames();
 >

## Matrices of zeros and ones...

How to most effectively generate all matrices from zeros and ones (matrices size 6 by 6), such that in each row and in each column exactly 4 units. This problem was encountered in solving one problem in the field of entertaining mathematics. I know how to solve it in about 100 seconds, but I so far do not give my solution so that everyone can enjoy solving it.

## for loop index is not evaluated as a number...

My "for loop" index is being treated as a letter and not a number. The 'h' in my for loop is is supposed to be the index for these tables but the result is tables that have indices of the letter 'h'.

The indexing for the 'Z' part works Z[h][1] ,Z[h][2] and Z[h][3] have numbers instead of the letter 'h' but the x1[h], y1[h] and Q[h][1],Q[h][2] and Q[h][3] are all 'h' indexed with no number as an index when I view this table in the variable viewer.

for h to 50 do :

Z[h][1] := s -> evalf(subs(x = x1[h](s), y = y1[h](s), Q[h][1])) ;

Z[h][2] := s -> evalf(subs(x = x1[h](s), y = y1[h](s), Q[h][2]));

Z[h][3] := s -> evalf(subs(x = x1[h](s), y = y1[h](s), Q[h][3]));

end do:

the result is just using the last value of index 'h' and puting it in the first index of 'Q'. There is nothing defined with index 51.

Z[2][3](4*(1/50));
Q[51][3]
Z[9][3](4*(1/50));
Q[51][3]

if I hard code the index numbers then it works correctly but I do not want to hard code all 50 of these.

Z[1][1] := s -> evalf(subs(x = x1[1](s), y = y1[1](s), Q[1][1]));
Z[1][1](4/50);
HFloat(-4.977040014616719)
Z[1][2] := s -> evalf(subs(x = x1[1](s), y = y1[1](s), Q[1][2]));
Z[1][2](3/50);
HFloat(-2.0000000000987943)
Z[1][3] := s -> evalf(subs(x = x1[1](s), y = y1[1](s), Q[1][3]));
Z[1][3](3/50);
1.563178208

Why is the for loop index variable 'h' treated as a letter and not evaluated to be a number in the indexing?

thanks . . .

## Breaking strength rope question...

Although a very general question... does the rope break or not?

A 100 kg weight is hung from the center of a 1/4" polypropelene rope making an angle of 10 degrees at both ends with the horizontal.  According to some characteristics, the breaking strength of the rope is 1125 lbs or 5kN.  The safe load (safety factor of 12) drops the weight to  93.8 lbs or 0.417kN. Find the tension in the rope?  Is it strong enough?

Fairly easy to solve in Maple - just two equations two unknowns making t1 tension on one side and t2 tension on the other side

eq1 := t1*cos(80*Pi*(1/180))+t2*cos(80*Pi*(1/180)) = 100*9.8 # ΣFy=mg

eq2 := t1*sin(80*Pi*(1/180))-t2*sin(80*Pi*(1/180)) = 0 #ΣFx=0 hence basically t1=t2

solve([eq1,eq2])

{t1 = 2821.797537, t2 = 2821.797537}

Therefore the tension on the rope t1=t2 is 2821 N  (looks like way beyond the safety factor) so this means the rope will not break, correct?  or is it that the total tension becomes t1+t2=5642 N putting us over the 5kN and the rope breaks?

## Determinant Function not working?...

Hi!
I'm very new to Maple, so I apologize ahead if this is a stupid question.

It seems that my "Determinant" function is not working properly, as shown in the picture.
I simply defined the matrix M and called for the determinant, as instructed by the help system in Maple.

Does anyone know what's happening?

Thank you very much.