Question

数列通项公式

1, 2+3, 4+5+6 ..... 求通项公式{an} 用什么方法做?

Answer 1

1,
2+3,
4+5+6,7+8+9+10,11+12+13+14+15.....
即
1*1,(1+1.5)*2
,(1+1.5+2.5)*3,(1+1.5+2.5+3.5)*4,(1+1.5+2.5+3.5+4.5)*5.....
即
1*1,(1+0.5*3)*2
,(1+0.5*3+0.5*5)*3,(1+0.5*3+0.5*5+0.5*7)*4,(1+0.5*3+0.5*5+0.5*7+0.5*9)*5.....
即
1*1,(1+0.5*3)*2
,[1+0.5*(3+5)]*3,[1+0.5*(3+5+7)]*4,[1+0.5*(3+5+7+9)]*5.....
观察：小括号内有(n-1)项，中间值为(n+1)
则有通项为
[1+0.5(n+1)(n-1)]n
即通项公式0.5n(n^2+1)