已知数列-1,4,-7,10...,(-1)的n次方乘以(3n-2),求其前n项和sn_数学解答

已知数列-1,4,-7,10...,(-1)的n次方乘以(3n-2),求其前n项和sn

人气：327 ℃　时间：2019-09-23 14:56:34

解答

当n为奇数时,Sn=-1+4-7+10-13+16+...+(3n-5)-(3n-2)=-(1+7+13+...+3n-2)+(4+10+16+...+3n-5)=-(1+3n-2)/2*(n+1)/2+(4+3n-5)/2*(n-1)/2=(3n-1)/4*[(n-1)-(n+1)]=(3n-1)/4*(-2)=-(3n-1)/2当n为偶数时,Sn=-1+4-7+10-13+...