因为1/n(n+1) = 1/n - 1/(n+1)
所以
1/2×1 + 1/2×3 + 1/3×4 + …… + 1/100×101
=(1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) +……+ (1/100 -1/101)
=1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +……+ 1/100 -1/101
=1 - 1/101
=100/101
1/2×1加1/2×3加1/3×4..100/101 等于?
2个回答
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