Question

A student decided to start saving money. On the first day he saved 1 cent, on the second day an additional 2 cents, on the third day he saved an additional 4 cents. Each day he doubled the amount he saved the previous day. How much would he have saved total on day 20 (in dollars)?'

Answer 1

$ 524.288

Step-by-step explanation:

We will use the sum of a geometric series;

S = (first term)(1-r^n)/(1-r)

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

= - (1 - 2^n)

= 2^n - 1

2 ^ (20 – 1)

2 ^ 19

= 524,288 cents

100 cents =  1 dollar

524,288 cents = 524,288/ 100 dollars

= $ 524.288