f(x)等于1除以括号里2的x次方加根号2求f(-5)+f(-4)+...f(5)+f(6)

问题描述:

f(x)等于1除以括号里2的x次方加根号2求f(-5)+f(-4)+...f(5)+f(6)

f(x)+f(1-x)=√2/2
所以
f(-5)+f(-4)+...f(5)+f(6)
=【f(-5)+f(6)】+……+【f(0)+f(1)】
=√2/2*6
=3√2

f(x)=1/[2^x+2^(1/2)]
f(x+1)=1/[2^(x+1)+2^(1/2)]
f(-x)=1/[2^(-x)+2^(1/2)]=2^x/[1+2^(x+1/2)]
f(x+1)+f(-x)=√2/2
所以f(-5)+f(-4)+...+f(0)+...+f(5)+f(6)= =3√2