Question

Question on comment

Answer 1

\[\sum_{k=1}^{\infty}(\dfrac{1}{k^q}-\dfrac{1}{(k+1)^q}) \] q>0

Answer 2

@satellite73

Answer 3

i think it is a telescoping sum

Answer 4

so all that will be left is the first term

Answer 5

\[\sum_{k=1}^{\infty}(\dfrac{1}{k^q}-\dfrac{1}{(k+1)^q})\] is one term minus the next term

Answer 6

but what is the logic?

Answer 7

Is there any algebraic way to find it out?

Answer 8

@SithsAndGiggles