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hmmmm...

hmmmm.....

\[a _{1} = 1\]
\[a _{n+1} = (\frac{ n+2 }{ n })a _{n}, n \ge 1\]
Find \[a _{30}\]
Careful . .

You are absolutely correct!

The way this particular recursive relation is set up, almost everything cancels.

At some point I will understand this... I have a few things before it to catch up on.

it is a triangle number :
1, 3, 6, 10, 15, 21, 28, ...., n/2 * (n+1)
so, a30 = 30/2 (30+1) = 465

That's true -- you can derive that the recursive formula generates triangular numbers.