1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.

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1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)

1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.
1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.

1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教.
您好
1/(1x3) = (1-1/3)/2
那么1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+.+(1/97-1/99)/2
=(1-1/3+1/3-1/5+1/5-1/7+.-1/97+1/97-1/99)/2
=(1-1/99)X2
=49/99