数列{an}的通项an=n^2(cos(n60^2-sinn60^2),其前n项和为Sn,则S30=

题目

数列{an}的通项an=n^2(cos(n60^2-sinn60^2),其前n项和为Sn,则S30=
2009 江西理 第8题

答案

an=n^2(cos(n60^2-sinn60^2)=n^2cos(2nπ/3),最小正周期2nπ/3=2π,n=3,cos(2nπ/3)的值{-1/2,-1/2,1,-1/2,-1/2,1┄┄┄},把一个周期看成一组,每组和的通项=-(3n-2)²/2-(3n-1)²/2+(3n)²=(18n-5)/2,组...