Question

For each positive integer n, let H _{n} = 1/1 +1/2 +⋯+ 1/n sum_{n=4}^{∞} 1/n*H_{n}*H_{n-1}=a/b for relatively prime positive integers a and b, find a+b

Answer 1

I reduced this problem to a primary school level problem here:

http://www.jiskha.com/display.cgi?id=1370534461

Answer 2

answer=????????

Answer 3

Read this:
http://en.wikipedia.org/wiki/Telescoping_series

Then sum both sides of:

1/H_{n} - 1/H_{n-1} =

-1/[n H_{n}H{n-1}]

from n = 4 to infinity, the left hand side is then a telescoping series.

Answer 4

answer===========

Answer 5

i have got the answer

Answer 6

what is the answer?
How do you do after that step?

Please explain

Answer 7

answer is 6/11 or 11+6= 17

Answer 8

Please stop cheating, mathslover. I will delete your account on Brilliant if you continue this behavior.

-Calvin

Answer 9

Do you know his account id Calvin? People like these are shame to the Brilliant community.

Answer 10

Mathslover,
Your account has been tracked on Brilliant. On suspicion of posting problems from Brilliant here, 20, 000 lifetime points will be deducted from your account after the next week.

Peter Taylor,
Brilliant Discussions Manager