I have recently queried WolframAlpha this way...

sum((1/(5*n+3)+1/(5*n+2))^2*(1/(5*n+4)+1/(5*n+1))^2*(3*n+1),-infinity<=n<=infinity)

...getting about -0.585507.

But the result is very different with queries like these ones...

sum((1/(5*n+3)+1/(5*n+2))^2*(1/(5*n+4)+1/(5*n+1))^2*(3*n+1),-1E20<=n<=1E20)
sum((1/(5*n+3)+1/(5*n+2))^2*(1/(5*n+4)+1/(5*n+1))^2*(3*n+1),-1E20<=n<1E20)
sum((1/(5*n+3)+1/(5*n+2))^2*(1/(5*n+4)+1/(5*n+1))^2*(3*n+1),-1E30<=n<=1E30)

... all giving about -1.09159.

I am not a mathematician, I can't understand the result -0.585507.