Evaluate $$\binom{n}{1} + 2\binom{n}{2} + 3 \binom{n}{3}+...+ n \binom{n}{n}$$
My attempt : I know $(a+b) ^n = \sum\limits_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$
But here Im confuse how to evaluate and im not able to proceed further.
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3did you mean $2\binom n2$ (to fit the pattern)? – J. W. Tanner Jun 14 '20 at 16:24
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1Usually a good starting place is to compute the expression for small $n$. Perhaps a pattern emerges. – lulu Jun 14 '20 at 16:25
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@J.W.Tanner yaa thanks u – jasmine Jun 14 '20 at 16:27
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1@jasmine hint: binomial theorem with a bit of calculus – Jun 14 '20 at 16:29