##### Question

# A goblin miner earns 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day

A goblin miner earns 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day. How much will the miner earn in 30 days?

Ok–I know to double the answer each time until 30–which would be:5,368,709.12

Is there an equation to make this easier?

Thanks

Sort of. Notice that on the nth day, the amount of money that day is 2^(n-1 ) Then notice the amount of money made to date (look at the above figures) is 2^(n-1) -1.

So the total the miner earns in thirty days…

2^29 + 2^29 -1= 2^30 -1 cents.

check that for n= 4, and n=5

Thank you!

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