This is a very difficult problem - please help!!!

Let h(n) and and S(n) be the partial sums of the harmonic and alternating harmonic series.
Show that S(2n) = h(2n) - h(n).

Question

This is a very difficult problem - please help!!!

Let h(n) and and S(n) be the partial sums of the harmonic and alternating harmonic series.
Show that S(2n) = h(2n) - h(n).

anonymous · Answer

Is this calling for an inductive proof? or just algebraic manipulation?

ns36 · Answer

Anything!

ns36 · Answer

I think algebraic manipulation would be preferable, though

anonymous · Answer

...er has your class talked about inductive proofs?  if not, its not worth going into.

ns36 · Answer

I have seen them before, but I'm not good enough at them to implement one here and we haven't talked about it at all in my math class.