Y by Math1331Math, Adventure10, Mango247
If
![\[
\sum_{n=1}^{\infty}\frac{\frac11 + \frac12 + \dots + \frac 1n}{\binom{n+100}{100}} = \frac pq
\]](//latex.artofproblemsolving.com/8/e/3/8e3f17c47b03a24998c1bdf8e8f4e8316a1afcca.png)
for relatively prime positive integers
, find
.
Proposed by Michael Kural
![\[
\sum_{n=1}^{\infty}\frac{\frac11 + \frac12 + \dots + \frac 1n}{\binom{n+100}{100}} = \frac pq
\]](http://latex.artofproblemsolving.com/8/e/3/8e3f17c47b03a24998c1bdf8e8f4e8316a1afcca.png)
for relatively prime positive integers


Proposed by Michael Kural
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