Graph Theory

The given expression is:

(1%20%2B%20x)%5E%7B101%7D%20(1%20-%20x%20%2B%20x%5E2)%5E%7B100%7D

Rewriting

(1%20-%20x%20%2B%20x%5E2)%5E%7B100%7D

as:

(1%20%2B%20x)(1%20%2B%20x%5E3)%5E%7B100%7D

Expanding:

(1%20%2B%20x)%20(1%20%2B%20x%5E3)%5E%7B100%7D

The coefficient of

x%5E%7B50%7D

in the given expansion is found by identifying terms contributing to

x%5E%7B50%7D

in the product. We need the coefficient of

x%5E%7B50%7D

in:

(1%20%2B%20x)%20(1%20%2B%20x%5E3)%5E%7B100%7D

This can be rewritten as:

%5Ctext%7BCoefficient%20of%20%7D%20x%5E%7B50%7D%20%5Ctext%7B%20in%20%7D%20(1%20%2B%20x%5E3)%5E%7B100%7D

Since

50

is not a multiple of

3

, there is no term contributing to

x%5E%7B50%7D

, so the coefficient is

0

. Final Answer:

%5Cboxed%7B0%7D

Chapter Questions
1 MCQs