1/4+1/28+1/70+.+1/8554=?
问题描述:
1/4+1/28+1/70+.+1/8554=?
答
1/4+1/28+1/70+.+1/8554=1/(1*4)+1/(4*7)+1/(7*10)+...+1/(91*94)=(1/3)*[3/(1*4)+3/(4*7)+3/(7*10)+...+3/(91*94)]=(1/3)*[(1-1/4)+(1/4-1/7)+(1/7-1/10)+...+(1/91-1/94)]=(1/3)*[1-1/94]=31/94