Question

Write the middle term in expansion of (2 x + 1/3)^10

Answer 1

Answer:

[896/81] * x⁵

Step-by-step explanation:

Total number of term in the binomial expansion of (A + X)n is (n + 1).

General term in binomial expansion is given by:

Tr+1 = nCr A^n-r X^r

If n is even number, the middle term is (m + 1)th term where m = n/2.

Hence, the middle term  Tm+1 = nCmA^n-mX^m

In the given equation, n = 10 => m = 5

T₆ = ¹⁰C₅ (2x)¹⁰⁻⁵.(1/3)⁵

     = 10!/5!(10-5)! * (2x)⁵ . (1/3)⁵

     = 252 * 32*x⁵/729 = 28*32/81 * x⁵ = [896/81] * x⁵