1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和

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1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和1/3+

1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和
1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和

1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和
=1/(3*1)+1/(5*3)+.+1/(2^n+1)(2^n-1)
=(1/1-1/3)/2+(1/3-1/5)/2+.+[1/(2^n-1)-1/(2^n+1)]/2
=[1/1-1/3+1/3-1/5+...+1/(2^n-1)-1/(2^n+1)]/2
=[1/1-1/(2^n+1)]/2
=[2^(n-1)]/[2^n+1]

1/2(1-1/3+1/3-1/5+...+1/(2^n-1)-1/(2^n+1))=1/2(1-1/(2^n+1))