已知数列an=2n-1,n为奇数,an=n+1,n为偶数,求该数列前n项和 Sn

n为奇数时,共有(n+1)/2个奇数项,(n-1)/2个偶数项.Sn=2[1+2+...+(n+1)/2]-(n+1)/2+2[1+2+...+(n-1)/2]+(n-1)/2 =2[(n+1)/2][(n+1)/2 +1]/2-(n+1)/2+2[(n-1)/2][(n-1)/2 +1]/2 +(n-1)/2=(n+1)²/4+(n+1)/2-(n+1)/2...