Solve the following. Find the ratio of nth terms of infinite series b and a: b_n /a_n , as n tends to infinity.
Given
a_{n+1} = a_n + 2* b_n , n>1.
b_{n+1} = a_n + b_n.
a_n * b_n > 0.
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b_{n+1}= a_n + b_n
a_{n+1} = a_n + 2 b_n
As n -> Infty, let x = b_n/a_n = b_{n+1} / a_{n+1}.
.
So x = (1+x)/(1+2x).
Thus x^2 = 1/2.
x = 1/sqrt(2).
a_{n+1} = a_n + 2 b_n
As n -> Infty, let x = b_n/a_n = b_{n+1} / a_{n+1}.
.
So x = (1+x)/(1+2x).
Thus x^2 = 1/2.
x = 1/sqrt(2).
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