1/2+1/6+1/12+1/20+.+1/72+1/90简算
问题描述:
1/2+1/6+1/12+1/20+.+1/72+1/90简算
答
原式=1/2 + (1/2-1/3) + (1/3-1/4) + (1/4-1/5) +…… + (1/8-1/9) + (1/9-1/10)
=1/2 +1/2-1/3 +1/3-1/4 +1/4 -1/5 +1/5+……+1/8-1/9+1/9-1/10
=1-1/10
=9/10