Finding an explicit formula for $a_n$ defined recursively by $a_{n+1}=2a_n\frac{(n+2)}{n+1} $

Question

for n = 1 ; $a_{1}= 1 $

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I tried to apply iteration to this recurrence relation with no success. How can I approach this?

Answer 1

Hint

$$a_{n+1}=2a_n\frac{(n+2)}{n+1}\implies \frac{a_{n+1}}{n+2}=2\frac{a_n}{n+1}$$

Define $b_n=\frac{a_n}{n+1}$ and this becomes quite simple.