逐欲天下
果实
共回答了3760个问题 举报
第n个加数为
1/(1+2+。。。+n)
=1/[(1+n)*n/2]
=2/[n*(n+1)]
1+1/3+1/6+1/10+1/15+...+1/5050
=2/(1*2)+2/(2*3)+3/(3*4)+...+2/(100*101)
=2*[1/(1*2)+1/(2*3)+...+1/(100*101)]
=2*(1-1/2+1/2-1/3+...+1/100-1/101)
=2*(1-1/101)
=2*100/101
=200/101
1年前
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