1/4+1/28+1/70+.+1/8554=?

1/4+1/28+1/70+.+1/8554=?
1/4+1/28+1/70+.+1/8554=?

1/4+1/28+1/70+.+1/8554=?
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

1/4+1/28+1/70+......+1/8554
=1/3×（3/4+3/28+3/70+......+3/8554）
=1/3×（1-1/4+1/4-1/7+1/7-1/10+1/10......-1/91+1/91-1/94）
=1/3×（1-1/94）
=91/282