设f(x)=2^x/(2^x+根号2),求f(1/n)+f(2/n)+f(3/n)+.+f(n/n)(n为自然数)如题,只要简要思路即可,

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设f(x)=2^x/(2^x+根号2),求f(1/n)+f(2/n)+f(3/n)+.+f(n/n)(n为自然数)如题,只要简要思路即可,
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设f(x)=2^x/(2^x+根号2),求f(1/n)+f(2/n)+f(3/n)+.+f(n/n)(n为自然数)如题,只要简要思路即可,
设f(x)=2^x/(2^x+根号2),求f(1/n)+f(2/n)+f(3/n)+.+f(n/n)(n为自然数)
如题,只要简要思路即可,

设f(x)=2^x/(2^x+根号2),求f(1/n)+f(2/n)+f(3/n)+.+f(n/n)(n为自然数)如题,只要简要思路即可,
f(1-x) = 2^(1-x)/(2^(1-x)+√2)
=2/(2+√2*2^x)
=√2/(2^x+√2)
=>
f(x)+f(1-x)=√2/(2^x+√2)+2^x/(2^x+√2)=1
2(f(1/n)+f(2/n)+f(3/n)+.+f((n-1)/n))
=(f(1/n)+f((n-1)/n))+(f(2)+f((n-2)/n))+……+(f((n-1)/n)+f(1/n))
=1+1+……+1 (n-1个1)
=n-1
f(n/n)=2-√2
=>
f(1/n)+f(2/n)+f(3/n)+.+f(n/n)
=2-√2+(n-1)/2
=1/2*n+3/2-√2