jmc

Question

If f(x)=x^(x+1)(x+2)^(x+3), then find the value of f(0)+f(-1)+f(-2)+f(-3).

Accepted Answer

Since 0^z=0 for any z>0, f(0) =f(-2)= 0. Since (-1)^0=1, align* f(0)+f(-1)+f(-2)+f(-3)&=(-1)^0(1)^2+(-3)^-2(-1)^0 &=1+1(-3)^2 = 109. align*