已知数列{an}满足a1=1,an+1={2an n为奇数,an+2,n为偶数},且a1+a3+a...

发布网友发布时间：2024-10-04 01:01

共1个回答

热心网友时间：2024-10-19 07:36

a(n+1)=an+2 ; n is even
= 2a(n-1) + 2
a(n+1) +2= 2(a(n-1) +2)
[a(n+1) +2]/(a(n-1) +2) =2
[a(n+1) +2] / (a1+2) = 2^(n/2)
a(n+1) +2 = 3.2^(n/2)
a(n+1) = -2+3.2^(n/2) ; n is even
n is even => n+1 is odd
an = -2+ 3.2^[(n-1)/2] ; n is odd

a1+a3+a5+......+a(2k-1)=3049
(-2+3.2^(0))+ (-2+3.2^(1)) +(-2+3.2^(2))+....+(-2+3.2^(k-1)) =3049
-2k + 3(2^k-1) =3049
k=10

热心网友时间：2024-10-19 07:38

a(n+1)=an+2 ; n is even
= 2a(n-1) + 2
a(n+1) +2= 2(a(n-1) +2)
[a(n+1) +2]/(a(n-1) +2) =2
[a(n+1) +2] / (a1+2) = 2^(n/2)
a(n+1) +2 = 3.2^(n/2)
a(n+1) = -2+3.2^(n/2) ; n is even
n is even => n+1 is odd
an = -2+ 3.2^[(n-1)/2] ; n is odd

a1+a3+a5+......+a(2k-1)=3049
(-2+3.2^(0))+ (-2+3.2^(1)) +(-2+3.2^(2))+....+(-2+3.2^(k-1)) =3049
-2k + 3(2^k-1) =3049
k=10

声明：本网页内容为用户发布，旨在传播知识，不代表本网认同其观点，若有侵权等问题请及时与本网联系，我们将在第一时间删除处理。E-MAIL:11247931@qq.com