How do you prove ∑ n = 1 ∞ 1 ( 2 n − 1...

ban1ka1u

ban1ka1u

Answered

2022-07-10

How do you prove
n = 1 1 ( 2 n 1 ) s = ( 2 s 1 ) ζ ( s ) 2 s
where s > 1

Answer & Explanation

postojahob

postojahob

Expert

2022-07-11Added 13 answers

Step 1
n = 1 1 ( 2 n 1 ) s + n = 1 1 ( 2 n ) s = ζ ( s )
n = 1 1 ( 2 n 1 ) s + 1 2 s n = 1 1 n s = ζ ( s )
This gives n = 1 1 ( 2 n 1 ) s + 1 2 s ζ ( s ) = ζ ( s ) . Can you finish? [The first equality folows by splitting 1 n s into even and odd terms].

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?