Question 145718
You can look at it this way:
Day 1 he earns 1 cent or {{{2^0}}} cents.
Day 2 he earns 2 cents or {{{2^1}}} cents.
Day 3 he earns 4 cents or {{{2^2}}} cents.
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.
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Day n he earns {{{2^(n-1)}}} cents.
The sum of these is expressed by:
{{{S = 2^0+2^2+2^3}}}+...{{{2^(n-1)}}}={{{2^n - 1}}} where n = the number of days worked.  Here, n = 20, so...
{{{S = 2^20 - 1 = 1048575}}}cents. Divide this by 100 to convert to dollars.
He earns a total of $10,485.75 for the 20 day's work.