Prove that the sum of the series C1C0-2C2C1 - 3C3C2 - - nCnCn -1 - nn -12-

C_1C_0=n1=n=C_2C_1=2n(n 1)2n=(n 1) ————— nC_nC_n 1=1n× n=1 ∴ n+1(n 1)+—— +1= sum of n consequent time integers =n(n+1)2 ...

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Greatest Binomial Coefficients

Prove that th...

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Prove that the sum of the series $\frac{C_{1}}{C_{0}} + 2 \frac{C_{2}}{C_{1}} + 3 \frac{C_{3}}{C_{2}} + . . . . + n \frac{C_{n}}{C_{n - 1}} = \frac{n (n + 1)}{2}$ .

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\frac{c_{1}}{c_{0}} + 2 \frac{c_{2}}{c_{1}} + 3 \frac{c_{3}}{c_{2}} + . . . . . . . . . + n \frac{c_{n}}{c_{n - 1}} = \frac{n (n + 1)}{2}

\frac{C_{1}}{C_{0}} + 2 \frac{C_{2}}{C_{1}} + 3 \frac{C_{3}}{C_{2}} + \dots \dots + n \frac{C_{n}}{C_{n - 1}} = \frac{n (n + 1)}{2}

c_{0}, c_{1}, c_{2}, . . . . . . . c_{n}

{(1 + x)}^{n}

\frac{c_{1}}{c_{0}} + \frac{2 c_{2}}{c_{1}} + \frac{3 c_{3}}{c_{2}} + . . . \frac{n c_{n}}{c_{n - 1}} = \frac{n (n + 1)}{2}

c_{0}, c_{1}, c_{2}, . . . . c_{n}

(1 + x)^{n}

\frac{c_{1}}{c_{0}} + \frac{2 c_{2}}{c_{1}} + \frac{3 c_{3}}{c_{2}} + . . . . . + \frac{n c_{n}}{c_{n - 1}} = \frac{n (n + 1)}{2}

C_{0}, C_{1}, C_{2}, . . . C_{n}

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\frac{C_{1}}{C_{0}} + 2 \frac{C_{2}}{C_{1}} + 3 \frac{C_{3}}{C_{2}} + . . . . + n \frac{C_{n}}{C_{n - 1}} = \frac{n (n + 1)}{2}

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