Prove $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$ using binomial and induction

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Can anyone help? I've got to prove

$$\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$$

using binomial first and then induction.

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By binomial theorem we obtain: $$\sum_{i=1}^n\binom{n}{i}i=\left(\sum_{i=1}^n\binom{n}{i}x^i\right)'_{x=1}=\left((1+x)^n\right)'_{x=1}=n(1+x)^{n-1}_{x=1}=n2^{n-1}.$$