An interesting equality

Calcul the sum is a very interesting subject, so I present to you this one. Can you solve it ?:D

Prove that: $\forall{n}\in{N}$ , $\displaystyle \sum_{i+j=n}C^i_n(i+1)^{i-1}(j+1)^{j-1}=2(n+2)^{n-1}$ .

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

go with pmi i.e principal of mathematical induction

Gagan Maheshwari - 8 years, 3 months ago

Can you write it down more clearly? Thanks!

Quan Dinh - 8 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$