Question

设f(x)=1/(2^x+1),求f(-3)+f(-2)+f(-1)+f(0)+f(1)+f(2)+f(3)

求详细解答
要求用简便方法,不代数

Answer 1

f(x) = 1/(2^x+1)
f(-x) = 1/[2^(-x) + 1] = 2^x/(1+2^x)
f(x) + f(-x) = (1 + 2^x)/(1+2^x) = 1
f(-3)+f(-2)+f(-1)+f(0)+f(1)+f(2)+f(3)
= f(-3) + f(3) + f(-2) + f(2) + f(-1) + f(1) + f(0)
=1+1+1+1/2 = 7/2