How much money would you have in 15 days if you get a penny doubled each day?

For the fifteen days,

1, 2, 4, 8, 16, 32, ...

Doubling continues until after the 15th day. But since counting started after 1 penny is given, so n for the sequence would have to be = 16.

This sequence is a GP common ratio = 4/2 = 2/1 = 2

Sum of nth term of GP = a (r^n - 1) / (r - 1)

where a = 1st term = 1,

n = 16, r = 2

Sum = 1 * (2^16 - 1) / (2 - 1)

= (2^16 - 1) / (1)

= (2^16 - 1) = 65536 - 1 = 65535

Money in 15 days = 65 536 pennies.