1/2+5/6+11/12+19/20+29/30+…+9701/9702+9899/9900.

问题描述:

1
2
+
5
6
+
11
12
+
19
20
+
29
30
+…+
9701
9702
+
9899
9900

12+56+1112+1920+2930+…+97019702+98999900=(1-12)+(1-16)+(1-112)+…+(1-19900)=1×99-(12+16+112+…+19900),=99-(11×2+12×3+13×4…+199×100),=99-(1-12+12-13+13−14+…+199-1100),=99-(1-...