The coefficient of x¹⁰ in the expansion of 1+(1+x)+ +(1+x)²⁰ is

Step-by-step solution

The given expression is a geometric series with first term a = 1 , common ratio r = (1+x) , and number of terms n = 21 . The sum of the series is S = a r^n - 1 r - 1 = 1 (1+x)²¹ - 1 (1+x) - 1 = (1+x)²¹ - 1 x . We need the coefficient of x¹⁰ in the expansion of S = (1+x)²¹ - 1 x . This is equivalent to finding the coefficient of x¹¹ in the expansion of (1+x)²¹ - 1 . The general term in the expansion of (1+x)²¹ is given by ²¹C_ r x^ r . For r = 11 , the term is ²¹C₁₁ x¹¹ . Since the constant term -1 does not affect t