Question

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

Answer 1

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+16+...-(3n-5)+(3n-2)

=-(1+7+13+...+3n-5)+(4+10+16+...+3n-2)

=-(1+3n-5)/2*n/2+(4+3n-2)/2*n/2

=n/4*[(3n+2)-(3n-4)]

=n/4*6

=3n/2