Question

将x/√(1+x²)展开成x的幂级数

Answer 1

f(x) = x/√(1+x^2) = [√(1+x^2)]'
= [1+x^2/2-x^4/(2*4)+x^6/(2*4*6)-x^8/(2*4*6*8)+.]'
= x-x^3/2+x^5/(2*4)-x^7/(1*4*6)+.(-1≤x≤1)