Question

Using the recursive formula, f(n+1)=2*f(n)+1, and given that f(1)=3, calculate the product of the digits in the number f(17).

Answer 1

looks like a lot of work
f(2) = f(1+1) = 2*f(1) +1 = 3
..
..
f(17) = ..

Answer 2

it's going to be lots of work

Answer 3

f(3) = 2*3+1 = 7
f(4) = 2*7+1 = 15
f(5) = 31
f(6) = 63
..

Answer 4

looks like 2^n-1

Answer 5

I'm getting 262143. If you want to check your work.

Answer 6

It's easy to note that. f(n)= 2^{n+1}-1

Answer 7

\[ f(n)= 2^{n+1}-1 \]

Answer 8

Or what he said.

Answer 9

Now I have memorized upto 2^{16} so here I have to do one small multiplication. but is there any way to do this in a less tedious way?

what if f(2434343) was asked? and instead of product it was asked as sum?