快速计算
(1)
1 1 1 1 1 1 1 1
1 = 1- 2 + 2 - 3 +
3 - 4 + 4
- 9 + 9
1 1
= (1 - 2 )+( 2
1 1
- 3 ) + ( 3 -
1
4 )+
1
+ ( 8
1 1
- 9 ) + 9
1 1 1 1 1 1 1 1 1
= 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 + 9
1 1 1 1 1
(2)原式 = 2×( + + + + + )
1 1 1 1 1 1 1
=2×[(1- 2 ) + ( 2 − 3 ) + ( 3 − 4 ) + ( 4 − 5 ) +
1
+( 100 −
1
101 )]
=2×[1- 1 ]
2
= 2 - 101
= 1 99
101
101