u^n / 1+u^2 < u^n
integrate both sides from 0~1
LHS becomes In, which is less than [1/n+1 u^(n+1) ](bounds from 0~1) = 1/n+1
hence In < 1/n+1
since In is above the x axis except at u=0, then the area represented by In is positive In>0
thus 0 < In < 1/n+1
hence 0 < I2n < 1/2n+1
limit as...