设数列{an}满足:若n=2k-1,(k∈N*),an=n,若n=2k,(k∈N*)an=ak求(1)a2+a4+a6+
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设数列{an}满足:若n=2k-1,(k∈N*),an=n,若n=2k,(k∈N*)an=ak求(1)a2+a4+a6+a8+a10+a12a+a14+a16
(1)原式=a1+a2+a3+a4+a5+a6+a7+a8
=a1+a1+a3+a1+a5+a3+a7+a1
=4a1+2a3+a5+a7
=4×1+2×3+5+7
=22
(2)Sn=a1+a2+a3++a2n−1+a2n
=(a1+a3+a5++a2n−1)+(a2+a4+a6++a2n)
=[1+3+5++(2n−1)]+(a2+a4+a6++a2n)
=4n−1+(a2+a4+a6++a2n)
=4n−1+(a1+a2++a2n−1)
=4n-1+Sn-1
链接在这里
=a1+a1+a3+a1+a5+a3+a7+a1
=4a1+2a3+a5+a7
=4×1+2×3+5+7
=22
(2)Sn=a1+a2+a3++a2n−1+a2n
=(a1+a3+a5++a2n−1)+(a2+a4+a6++a2n)
=[1+3+5++(2n−1)]+(a2+a4+a6++a2n)
=4n−1+(a2+a4+a6++a2n)
=4n−1+(a1+a2++a2n−1)
=4n-1+Sn-1
链接在这里
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