Unfamiliar Reciprocals

True or False?

\[ \large \sum_{i=0}^n \dfrac1{ {n \choose i} } =\frac{n+1}{2^{n+1}} \sum_{i=1}^{n+1} \frac{2^i}i \]

Notation: \( \dbinom MN = \dfrac {M!}{N! (M-N)!}\) denotes the binomial coefficient.

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