1.
=1/2+1+[1/2×(4+1)] + [1/2×(5+1)] + …… + [1/2×(60+1)]
=1/2+1+ 1/2×(5+6+……+61)
=1/2+1+ 1/2×(1+2+……+61) - 1/2×(1+2+3+4)
=1/2+1+ 1/2×1891 - 1/2×10
=1/2×(1+2+1891-10)
=942
上面用到了1+2+3+……+n = n(n+1)/2这个公式
2.
=(1/8-1/9)+(1/9-1/10)+……+(1/99-1/100)
=1/8-1/100
=23/200
提示 1/n*(n+1) = 1/n - 1/(n+1)