Find closed form of a sequence $2,5,11,23,\dots$
How to get generating function for this sequence (closed form)?
Explicit form is $f(x)=2+5x+11x^2+23x^3+\cdots$
Is it possible to get to geometric series representation?
I tried to derive the series multiple times, but that doesn't help.
Could someone give a hint?
Best Answer
Hint Adding $1$ to each term of the sequence gives $$3, 6, 12, 24, \ldots,$$ and dividing each term of this new series by $3$ gives $$1, 2, 4, 8, \ldots .$$
On the other hand, $1 + x + x^2 + x^3 + \cdots$ is the series for the function $x \mapsto \frac{1}{1 - x}$.