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.