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1/2+1/4+1/8+1/16+1/32+1/64=

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1/2+1/4+1/8+1/16+1/32+1/64=
1/2+1/4+1/8+1/16+1/32+1/64
=(32+16+8+4+2+1)/64
=63/64;
1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/6)-(1/7)
=1-(1/7)
=6/7.
是否可以解决您的问题?