急求高一数学数列题,详细过程!

an/a(n-1)=2^n,
a2/a1=2^2
a3/a2=2^3
a4/a3=2^4
……
a100/a99=2^100 叠乘
a100/a1=2^(2+3+4+……+100) a100=2^[5049]
an/a1=2^(2+3+4+……+n)=2^((n+2)*(n-1)/2)
an=2a(n-1)+1
[an+1]=2[a(n-1)+1]
bn=an+1 b(n-1)=a(n-1)+1
bn=2b(n-1) 是等比数列
b1=a1+1
bn=b1*2^(n-1)
an+1=(a1+1)*2^(n-1) an=(a1+1)*2^(n-1)-1
1/(2n-1)(2n+1)=1/2[1/(2n-1)-1/(2n+1)]
1/3=1/2[1-1/3] 1/5=1/2[1/3-1/5] ……
S=1/1*3+1/3*5+1/5*7...+1/(2n-1)(2n+1)
=1/2[1/3-1/5+1/5-1/7+1/7-1/9+……+1/(2n-1)-1/(2n+1)]
=1/2[1/1/(2n+1)]
=n/(2n+1)