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.
