7.Binomial Theorem
medium

$\frac{{{C_1}}}{{{C_0}}} + 2\frac{{{C_2}}}{{{C_1}}} + 3\frac{{{C_3}}}{{{C_2}}} + .... + 15\frac{{{C_{15}}}}{{{C_{14}}}} = $

A

$100$

B

$120$

C

$- 120$

D

इनमें से कोई नहीं

(IIT-1962)

Solution

हम जानते हैं कि

$\frac{{{C_1}}}{{{C_0}}} + 2\frac{{{C_2}}}{{{C_1}}} + 3\frac{{{C_3}}}{{{C_2}}} + …. + n.\frac{{{C_n}}}{{{C_{n – 1}}}} = \frac{{n(n + 1)}}{2}$

$ n=15 $ रखने पर,  $\frac{{15 \times (15 + 1)}}{2} = 120$.

Standard 11
Mathematics

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