How to prove: ∑k=1∞k−12k(1+k)(1+2k)=loge8−2

Yahir Haas

Yahir Haas

Answered

2022-01-21

How to prove:
k=1k12k(1+k)(1+2k)=loge82

Answer & Explanation

sjkuzy5

sjkuzy5

Expert

2022-01-22Added 11 answers

Let me try. Note that the
RHS=3ln2+2=2+3k=1(1)k+1k=2+3k=112k112k
We have
k=1k12k(k+1)(2k+1)=k=12k(k+1)2k(k+1)(2k+1)
=k=1(1(k+1)(2k+1)12k(2k+1))
=k=1(22k+11k+112k+12k+1)
=2+3k=112k112k
=RHS

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?