I tried it by showing that true for r=0 and then assuming it to be true for r=k and trying to show it true for r=k+1. But I was not able to do that efficiently. So, please help me get a way out of it...
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1Please post what you did and where you faced problems. – Vizag Apr 19 '19 at 18:43
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After putting r=k+1, I got the expression as {n(n+1)(n+2)...(n+k)}/(k+1)! . Now I don't know how to approach further.. – Apoorv Apr 19 '19 at 18:49
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What have you tried so far? – little o Apr 19 '19 at 18:50
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2the binomial coefficient $\binom{n+r-1}{r}=\frac{(n+r-1)!}{r!(n-1)!}=\frac{n(n+1)...(n+r-1)}{r!}$ is integer. – user614287 Apr 19 '19 at 19:08
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Welcome to MSE. Please edit and use MathJax to properly format math expression. Also, a friendly advice: title should NOT be the first sentence of your question. In particular, see the last bullet. – Lee David Chung Lin Apr 20 '19 at 01:19