Scheming
A fraudster creates a new scheme. It nets him $1,000 during the first week, $2,000 during the second week, $4,000 during the third week, and so on, doubling every week.
How many weeks will it take for him to accumulate over a million dollars with his scheme?
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2 solutions
I wish I could get that much money
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Go talk to Bernie Madoff and ask him for assistance in creating a scheme. :)
It's GP.
a = 1 0 0 0 , r = 2 S n = 1 − 2 1 0 0 0 ( 1 − 2 n ) 1 0 0 0 0 0 0 = − 1 1 0 0 0 ( 1 − 2 n ) − 1 0 0 0 = 1 − 2 n 2 n = 1 0 0 1 n ≈ 9 . 9 6 ∴ n = 1 0 ⟹ S n > 1 0 0 0 0 0 0
The cumulative total:
After week 1 --1000 dollars
After week 2 -- 3000 dollars
After week 3 -- 7000 dollars
After week N, the accumulated total is ( 2 N − 1 ) × 1 0 0 0 dollars.
This becomes more than a million dollars at N = 10.