数列{an}的通项an=n²(cos²nπ/3-sin²nπ/3),其前n项为Sn,则S30为?
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an=n²(cos²nπ/3-sin²nπ/3)=n²cos2nπ/3
则cos2π/3=-1/2;cos4π/3=-1/2;cos6π/3=1;
cos8π/3=-1/2;cos10π/3=-1/2;cos12π/3=1;
(-1/2)×n²+(-1/2)×(n+1)²+(n+2)²=3n+7/2
故S30=(-1/2)×1²+(-1/2)×2²+3²+ =3×1+7/2
(-1/2)×4²+(-1/2)×5²+6²+ =3×4+7/2
。。。。。。 。。。。。。。
(-1/2)×28²+(-1/2)×29²+30² =3×28+7/2
=3×(1+28)×10/2+10×7/2
=435+35=470
则cos2π/3=-1/2;cos4π/3=-1/2;cos6π/3=1;
cos8π/3=-1/2;cos10π/3=-1/2;cos12π/3=1;
(-1/2)×n²+(-1/2)×(n+1)²+(n+2)²=3n+7/2
故S30=(-1/2)×1²+(-1/2)×2²+3²+ =3×1+7/2
(-1/2)×4²+(-1/2)×5²+6²+ =3×4+7/2
。。。。。。 。。。。。。。
(-1/2)×28²+(-1/2)×29²+30² =3×28+7/2
=3×(1+28)×10/2+10×7/2
=435+35=470
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