一个数列﹛an﹜,当n为奇数时,an=5n+1,当n为偶数时,an=2的2/n次,求这个数列的前n项之和。
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n=2k时,Sn=S2k=【a1+a3+……+a2k-1]+[a2+a4+……+a2k]
=【6+16+……+10k-4】+【2^1+2^2+……+2^k]
=(6+10k-4)*k/2+2*(2^k-1)/(2-1)=(5k+1)*k+2^(K+1)-2
=5n^2/4+n/亏盯2+2^(0.5n+1)-2;
n=2k-1时睁档,Sn=S2k-a2k=(5k+1)*k+2^(K+1)-2-2^k=5(n+1)^2/4+(n+1)/2+2^(销早和0.5n+0.5)-2
=【6+16+……+10k-4】+【2^1+2^2+……+2^k]
=(6+10k-4)*k/2+2*(2^k-1)/(2-1)=(5k+1)*k+2^(K+1)-2
=5n^2/4+n/亏盯2+2^(0.5n+1)-2;
n=2k-1时睁档,Sn=S2k-a2k=(5k+1)*k+2^(K+1)-2-2^k=5(n+1)^2/4+(n+1)/2+2^(销早和0.5n+0.5)-2
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