SOLUTION: A(n)=1 + 3/2 + 5/4 + 7/8 +...... +(2n+1)/2^n / lim A(n) (n->+inf)
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Question 1113261: A(n)=1 + 3/2 + 5/4 + 7/8 +...... +(2n+1)/2^n / lim A(n) (n->+inf)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The indeterminate form is 
so apply L'Hôpital
}{\frac{d}{dn}\(2^n\)})
})
})
The limit of a constant times a function is equal to the constant times the limit of the function, so:
}\,\cdot\,\lim_{n\right\infty}\ \(2^1\,\cdot\,2^{-n}\)\ =\ \frac{2}{\ln(2)}\,\cdot\,\lim_{n\right\infty}\ 2^{-n})
I don't know how rigorous you need to get with this. I'm satisfied that the limit is zero, but if you want to be absolutely correct, you need to use the chain rule for limits so you ultimately end up with 
John
My calculator said it, I believe it, that settles it
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