limit question:

假設,你說的是
Please prove the statement for n>=0.n是一個整數(不然,2個變數我未學=.=)
方便D
我改一改D變數
Prove: lim n to INFINITEY, (1^k + 2^k +....+ n^k)/ n^(k+1) =1/(k+1)
由(0至n)integration (x^k)dx<1^k + 2^k +....+ n^k<由(0至n) integration [(x+1)^k]dx
[n^(k+1)]/(k+1)<1^k + 2^k +....+ n^k<[(n+1)^(k+1)]/(k+1)
除n^(k+1)
1/(k+1)<[1^k + 2^k +....+ n^k]/n^(k+1)<[(1+1/n)^(k+1)]/(k+1)
lim n to INFINITEY,1/(k+1)=1/(k+1)
lim n to INFINITEY,[(1+1/n)^(k+1)]/(k+1)=1/(k+1)
三文冶一夾
得,得左
美源髮彩,冇得彈
lim n to INFINITEY,(1^k + 2^k +....+ n^k)/ n^(k+1) =1/(k+1)

果個integration呢,你畫個圖就明架啦

If n=-2
L.H.S.
= lim X to INFINITEY (1 + 1/2^2 + 1/3^2 +...)/ X^(-2+1)
= lim X to INFINITEY (pi^2 /6)X
= INFINITEY
R.H.S.
= 1/(-2+1)
= -1
L.H.S. =/= R.H.S.
So it is wrong!