1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3······+100)
=1/(3×2/2)+1/(4×3/2)+1/(5×4/2)+······+1/(101×100/2)
=2×[1/(2×3)+1/(3×4)+1/(4×5)+······+1/(100×101)]
=2×[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+······+(1/100-1/101)]
=2×(1/2-1/101)
=1-2/101
=99/101
注:应注意括号的正确使用,以免造成误解。
你的提问有些模糊
1/1+2还是1/(1+2)
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