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

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

Count Iblis · Answer

I reduced this problem to a primary school level problem here: http://www.jiskha.com/display.cgi?id=1370534461

mathslover · Answer

answer=????????

Count Iblis · Answer

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.

mathslover · Answer

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

mathslover · Answer

i have got the answer

help me · Answer

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

rohit · Answer

answer is 6/11 or 11+6= 17

Andrew · Answer

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

Shame · Answer

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

Peter Taylor · Answer

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