Question

Q. If the sum of the coefficients in the expansion of ( 1+2x)n is 6561, the greatest term in the expansion for
x = 1/2 is
(A) 4th (B) 5th (C) 6th (D) none of these

Answer 1

5th Term would be greatest

Step-by-step explanation:

(1 + 2x)ⁿ = ⁿC₀  +  ⁿC₁(2x) + ⁿC₂(2x)² +.......................+ⁿCₙ(2x)ⁿ

putting x = 1

(1 + 2)ⁿ = ⁿC₀  +  2 * ⁿC₁ + 2² * ⁿC₂  +.......................2ⁿ * ⁿCₙ

=> 3ⁿ = 6561

=> n = 8

Greatest term in expansion would be the middle term

Hence 5th Term would be greatest

Learn more:

The first three terms in the binomial expansion of ( ) n x y + are 1, 56 ...

https://brainly.in/question/13197893

Use binomial theorem to expand (2+X)5 in ascending powers of x ...

https://brainly.in/question/11212431