Question

这种分奇偶的数列一直不太会，请大神指点迷津，谢谢谢谢谢谢谢谢啦啦啦

Answer 1

a1=1
a(n+1)
=an +1 ; n是奇数
=an + 2 ；n是偶数
(1)
bn = a(2n)
b1=a2= a1+1 = 1+1=2
b2
=a4
= a3+1
= (a2+2) +1
= (2+2)+1
=5
bn

= a(2n)
= a(2n-1) +1
= [a(2n-2) +2 ] +1
=a(2n-2) +(1+2)
=[a(2n-3) +1] +(1+2)
=[a(2n-4)+2 ] +(1+1+2)
=a(2n-4)+2(1+2)
=...
=a2 + 3(n-1)
=2+ 3(n-1)
=3n-1
(2)

Sn=a1+a2+...+an
S20
=a1+a2+...+a20
=(b1+b2+...+b10)+ (a1+a3+...+a19)
=(b1+b2+...+b10)+ 1+(a3+a5+...+a19)
=(b1+b2+...+b10)+ 1+[(a2+2)+(a4+2)+...+(a18+2)]
=(b1+b2+...+b10)+ 19+(a2+a4+...+a18)
=(b1+b2+...+b10)+ 19+(b1+b2+...+b9)
=5(b1+b10) + 19 + (9/2)(b1+b9)
=5(2+29) +19+(9/2)(2+26)
=300