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
I reduced this problem to a primary school level problem here:
http://www.jiskha.com/display.cgi?id=1370534461
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.
answer===========
i have got the answer
what is the answer?
How do you do after that step?
Please explain
answer is 6/11 or 11+6= 17
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