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

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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.

Answers (1)

George Papazafeiropoulos
George Papazafeiropoulos on 28 May 2014
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.

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