1+1/3+1/6+1/10+...1/5050

(1+1/3+1/+6+1/10+...1/5050)
=2*(1/2++1/6+1/12+1/20+...+1/10100)
=2*[1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(100*101)]
=2*[(2-1)/(2*1)+(3-2)/(2*3)+(4-3)/(3*4)+(5-4)/(4*5)+...+(101-100)/(100*101)]
=2*[1-1/2+1/2-1/3+1/3-1/4+...+1/100-1/101]
=2*(1-1/101)
=200/101

=2(1/2+1/6+1/12+1/20+...+1/10100)
=2[1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(100*101)]
=2[(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/100-1/101)]
=2(1-1/101)
=200/101

1=2（1/1-1/2）
1/3=2（1/2-1/3）
1/6=2（1/3-1/4）
。。。。。。。
1/5050=2（1/100-1/101
1+1/3+1/6+1/10+...1/5050=200/101
如果你学过数列就好办了