Hi all!

I been working on series test, I wanted to ask about a step which I don't get. Heres the series:

1/5 + 2/6 + 2^2/7 + 2^3/8 + 2^4/9 + ...

applying the ratio test:

Un = 2^(n-1)/(4+n), Un+1 = 2^n/(5+n)

so therefore, Un+1 / Un = 2^n/(5+n).(4+n)/2^(n-1)

using the rule 2^(n-1) = 2^n.2^-1

the 2^n cancels leaving 2^-1, but I don't know how to get:

Un+1 / Un = 2(4+n)/(5+n)

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I'm having the same problem with another question to where:

Un = 2n-1/2^(n-1), Un+1 = 2n+1/2^n

Un+1 / Un = 2n+1/2^n.2^(n-1)/2n-1

I don't get how to get

Un+1 / Un = 1/2.2n+1/2n-1

Thank you.