Question

2²-1²=3 3²-2²=5 找出第n个式子 用规律计算 1+3+5+7+..........+2009+2011

Answer 1

4^2-3^2=7
....
n^2-(n-1)^2=2n-1
1+3+5+7+.......+2009+2011
=1^2+(2²-1²)+(3²-2²)+(4^2-3^2)+......+(1005^2-1004^2)+(1006^2-1005^2)
=1006^2
=1012036

Answer 2

1+3+5+7+9+……+2009+2011
=1²﹢﹙2²-1²﹚+﹙3²-2²﹚+﹙4²-3²﹚+……+﹙1005²-1004²）＋﹙1006²-1005²﹚
=1²+2²-1²+3²-2²+4²-3²+……+1005²-1004²+1006²-1005²
=1006²