What is _ x 0 (1+x)^n-1 x equal to?

Step-by-step solution

aligned & _ x 0 (1+x)^n-1 x & (1+x)^1-1 x = 1+x-1 x = x x =1 & (1+x)^2-1 x = 1+2 x+x^2-1 x = x(2+x) x aligned aligned (1+x)^3-1 x & = 1+3 x+3 x^2+x^3-1 x & = 3 x+3 x^2+x^3 x = x (3+3 x+x^2 ) x _ x 0 (1+x)^n-1 x & = 1+n x+ -1 x & = n x+ highest power of x x & = x(n+ highest power of x) x & =n+ highest power of x & =n aligned