数列an=n^2((cos(nπ/3))^2-(sin(nπ/3))^2)
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数列an=n^2((cos(nπ/3))^2-(sin(nπ/3))^2)
求S30
好像是470
教教我
求S30
好像是470
教教我
之前你出过这种题了吧,原来让求的是前30项.也不说清楚是从a0还是a1开始,不过不要紧a0 = 0; 之前求的是S29,S30如下
cos(nπ/3)^2 - sin(nπ/3)^2 = 1 - 2sin(nπ/3)^2 周期为3
从n=0开始:1,-1/2 ,-1/2,.
所以前三十项和为
a0+...+a29 = -1/2*(0^2+.+29^2) + 3/2*(0^2+3^2+.+27^2)
= -1/2*(29*30*59)/6 + 27/2*(1^2+.+9^2)
= -(29*5*59)/2 + 27/2 *(9*10*19)/6
= (-8555+7695)/2 = -430
S30 = 上面求出的结果再 + a30 = -430 + 900 = 470
cos(nπ/3)^2 - sin(nπ/3)^2 = 1 - 2sin(nπ/3)^2 周期为3
从n=0开始:1,-1/2 ,-1/2,.
所以前三十项和为
a0+...+a29 = -1/2*(0^2+.+29^2) + 3/2*(0^2+3^2+.+27^2)
= -1/2*(29*30*59)/6 + 27/2*(1^2+.+9^2)
= -(29*5*59)/2 + 27/2 *(9*10*19)/6
= (-8555+7695)/2 = -430
S30 = 上面求出的结果再 + a30 = -430 + 900 = 470
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