(1)
Sn=2an-1
n=1 => a1=1
for n>=2
an = Sn -S(n-1)
an = 2an - 2a(n-1)
an =2a(n-1)
an = 2^(n-1) .a1
=2^(n-1)
bn=b1+(n-1)d
b1=a1=1
b4=a3
b1+3d = 4
1+3d=4
d=1
bn=n
(2)
cn = 1/an + 2/[bn.b(n+1)]
= 1/2^(n-1) + 2/[n(n+1)]
= 1/2^(n-1) + 2[ 1/n- 1/(n+1)]
Tn = c1+c2+...+cn
= 2(1- 1/2^n) + 2[ 1 - 1/(n+1) ]
=4 - 2/(n+1) - 1/2^(n-1)
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