Help me about the error with symsum function to calculate the sum of series ?

I use symsum to calculate the sum of a series, with 1) and 2), it's ok. but with 3), the symsum does not have the result. Why ? help me about this error. Thanks very much.

Answer 1

[George Papazafeiropoulos]

Maybe because there is not any analytical formula which gives this sum. Can this function be integrated in an analytic way? I suppose no.

You can take the numerical result of the sum in this way:

k=1:10000;
sum1=sum(((k+1).^(1/2) - (k-1).^(1/2))./k.^2);
k=1:100000;
sum2=sum(((k+1).^(1/2) - (k-1).^(1/2))./k.^2);

and compare sum1 and sum2. The result is 1.763306701885209.