Question

(1 + x) ³ + (1 + x) ⁶ + (1 + x) ⁷ + .... + (1 + x)⁵⁰ Coefficient of x ^ 50





Answer with Solution​

Answer 1

Answer:

Coefficient of x⁵⁰ = 1

Step-by-step explanation:

The only place from where you can get x⁵⁰ term will be from the last term of the series, i.e. (1+x)⁵⁰. This is because the other terms will give coefficients less than x⁵⁰

Let us assume expansion of (1+x)²

We get 1+2x+x²

Now, assume the expansion of (1+x)³

We get 1+3x+3x²+x³

We find that for the expansion of (ax+by)^n, the term without x, and the term with the highest power of x have coefficients as 1, if and only if both a and b equals to 1

Now, in the expansion of (1+x)⁵⁰, we will get x⁵⁰ coefficient as 1 with the logic I have mentioned above.

Hope it helps