Question

設(shè)曲線y=xn(1-x)在x=2處的切線與y軸交點的縱坐標(biāo)為an,則數(shù)列{}的前n項和Sn等于　　　　.

 

Answer 1

2n+1-2

【解析】∵y'=nxn-1-(n+1)xn,∴y'|x=2=n·2n-1-(n+1)·2n=-n·2n-1-2n,

∴切線方程為y+2n=(-n·2n-1-2n)(x-2),

令x=0得y=(n+1)·2n,即an=(n+1)·2n,

∴=2n,∴Sn=2n+1-2.