用數(shù)學(xué)歸納法.
n=0時,
t^n-nt+(n-1)=1-0+（0-1）=0滿足≥0.
假設(shè)對n=任意自然數(shù)k,t>0,滿足t^k-kt+(k-1)≥0
n=k+1時,
t^(k+1)-(k+1)t+(k+1-1)
=t*t^k-k*t-t+k
=t*(t^k-kt+k-1) + k*t*t-2kt + k
=t*(t^k-kt+k-1) + k*(t^2-2t+1)
=t*(t^k-kt+k-1) +k*(t-1)^2
>=0 + k*(t-1)^2
>= 0