设f(x)=x^2-ln(x+1)(1)当x>0,求证f(x)0)当n∈N*时,求证∑f(1/k)
问题描述:
设f(x)=x^2-ln(x+1)(1)当x>0,求证f(x)0)
当n∈N*时,求证∑f(1/k)
答
设F(x)=x^2-ln(x+1)-x^3
F'(x)=2x-1/(x+1)-3x^2=(-1/(x+1))(3x^3+(x-1)^2)0)
F(0)=1-0-1=0
F(x)0)
f(1/k)