作业帮求数列通项
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求数列通项
求数列通项
求数列通项
a(n+1) = [(4n+6)an +4n+10]/(2n+1)
(2n+1)a(n+1) = (4n+6)an +4n+10
(2n+1)[a(n+1)+2] = (4n+6)][an +2]
[a(n+1)+2]/[an +2] =(4n+6)/(2n+1)
[an+2]/[a(n-1) +2] =(4n+2)/(2n-1)
= 2 + 4/(2n-1)
(an+2)/(a1 +2) = 2(n-1) + 4[ 1/3+1/5+...+1/(2n-1) ]
an + 2 = (a+2) {2(n-1) + 4[ 1/3+1/5+...+1/(2n-1) ] }
an = -2+ (a+2) {2(n-1) + 4[ 1/3+1/5+...+1/(2n-1) ] }