Find coefficient of x⁴⁸ in:
(1+x)² + 2(1+x)³ + 3(1+x)⁴ + ... + 100(1+x)¹⁰⁰

Solution:

General term:
r(1+x)^(r+1)

Coefficient of x⁴⁸:

Σ r × C(r+1,48)

After simplification:

Coefficient =
101C49 − 100C50

Answer: 101C49 − 100C50