Question

What is the sum of coefficients in the expansion of (3+2x)^99?

Answer 1

Answer:

5⁹⁹

Step-by-step explanation:

Here we need to find sum of  the coefficients in the expression (3+2x)⁹⁹.

As we know the Binomial expression of  (3+2x)⁹⁹ is

 (3+2x)⁹⁹ = ⁹⁹C₀(2x)⁹⁹ + ⁹⁹C₁(3)¹(2x)⁹⁸ + ⁹⁹C₂(3)²(2x)⁹⁷+ ......+⁹⁹C₉₉(3)⁹⁹

Now to find the sum of all coefficients in the expression we put x =1. Because that will add all the coefficients in the expression , so the sum will be

(3+2*1)⁹⁹ =  ⁹⁹C₀(2*1)⁹⁹ + ⁹⁹C₁(3)¹(2*1)⁹⁸ + ⁹⁹C₂(3)²(2*1)⁹⁷+ ......+⁹⁹C₉₉(3)⁹⁹

Thus sum of coefficients  = (3+2)⁹⁹ = 5⁹⁹