Question

The coefficient of x⁵ in the expansion of (1 + x)²¹ + (1 + x)²² +.........+(1 + x)³⁰ is

(a)   ³¹ C₅ – ²¹C₅

(b)   ³¹C₆  –  ²¹C₆ 

(c)   ³⁰C₆ – ²⁰C6 

(d)   None of these 

Answer 1

Correct option   (b) ³¹C₆ – ²¹C₆

Explanation:

Co-efficient of x⁵ in (1 + x)²¹ + (1 + x)²² +............+ (1 + x)³⁰ 

= Co-efficient of x⁵ in  (1 + x)²¹{(1 + x)¹⁰ -1}/(1 + x) - 1

coefficient of x⁶ in (1 + x)³¹ – (1 + x)²¹  is ³¹C₆ - ²¹C₆