C_1 C_0 + 2 C_2 C_1 + 3 C_3 C_2 + .... + 15 C_ 15 C_ 14 = - Vidyadip

MCQ

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

A
$100$
✓
$120$
C
$- 120$
D
None of these

✓

Answer

Correct option: B.

$120$

b
(b) We know that

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

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

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