SOLUTION: a worker is hired for 20 days. on the first day he makes 1 cent on the 2nd day he makes 2 cents and the pay doubles each day. What is the total pay?

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Question 145718: a worker is hired for 20 days. on the first day he makes 1 cent on the 2nd day he makes 2 cents and the pay doubles each day. What is the total pay?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can look at it this way:
Day 1 he earns 1 cent or 2%5E0 cents.
Day 2 he earns 2 cents or 2%5E1 cents.
Day 3 he earns 4 cents or 2%5E2 cents.
.
.
.
Day n he earns 2%5E%28n-1%29 cents.
The sum of these is expressed by:
S+=+2%5E0%2B2%5E2%2B2%5E3+...2%5E%28n-1%29=2%5En+-+1 where n = the number of days worked. Here, n = 20, so...
S+=+2%5E20+-+1+=+1048575cents. Divide this by 100 to convert to dollars.
He earns a total of $10,485.75 for the 20 day's work.