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Question: question on sum. Trying to obtain zero for this sum.

Question:question on sum. Trying to obtain zero for this sum.

nm 9934 Maple 2019
sum
November 24 2019
0

Hello;

What trick if any is needed to obtain zero for this sum in Maple?

sum(sin(Pi*n/2)*sin(n*Pi*(x + 1)/2)*cos(n*Pi*t/2),n=1..infinity)

The above sum, according to Mathematica is zero. I am trying to see if same result can be obtained by Maple in order to verify this result. It is possible ofcourse that Mathematica result is not correct. I am also trying to verify the sum is zero by hand, but no success so far.

> 

mySum:=sum(sin(Pi*n/2)*sin(n*Pi*(x + 1)/2)*cos(n*Pi*t/2),n=1..infinity)

sum(sin((1/2)*Pi*n)*sin((1/2)*n*Pi*(x+1))*cos((1/2)*n*Pi*t), n = 1 .. infinity)

> 

value(mySum)

sum(sin((1/2)*Pi*n)*sin((1/2)*n*Pi*(x+1))*cos((1/2)*n*Pi*t), n = 1 .. infinity)

> 

simplify(mySum)

sum(sin((1/2)*Pi*n)*sin((1/2)*n*Pi*(x+1))*cos((1/2)*n*Pi*t), n = 1 .. infinity)

> 

 


Here is Mathematica result

Using Maple 2019.2 on windows 10. 

Thanks

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