Question

Find the coefficients of x^7 expansion of (1+x)+(1+x)² + ... + (1+x)¹⁰.​

Answer 1

Hi,

165

Explanation:

`\displaystyle (1+x)+(1+x)^2+...+(1+x)^(10)\\\\=\sum_(j=1)^(10) (1+x)^j-1\\\\=((1+x)^(11)-1)/((1+x)-1) -1\\\\\\=((1+x)^(11)-1)/(x) -1\\\\=x^(10)+11*x^9+55*x^8+165*x^7+330*x^6+462*x^*5+462*x^4+330*x^3+165*x^2+55*x+10\\`