Crazy Expression

Algebra Level 3

( 2 ( 2 ( 2 ( ⋯ ( 2 ( 2 ( 2 ⏟ Number of 2’s = 17 + 1 ) + 1 ) + 1 ) + ⋯ + 1 ) + 1 ) + 1 ⏟ Number of 1’s = 17 ) (\underbrace{2(2(2(\cdots(2(2(2}_{\text{Number of 2's = 17}}+\underbrace{1)+1)+1)+\cdots+1)+1)+1}_{\text{Number of 1's = 17}})

The above shows a long, nested expression with seventeen 1's and seventeen 2's.

Evaluate this expression.

2 18 − 1 2^{18} - 1 2 19 − 1 2^{19} - 1 2 17 − 1 2^{17} - 1 2 20 − 1 2^{20} - 1

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Micah Gadbois by Micah Gadbois , 15, USA

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1 solution

Azadali Jivani
Jul 21, 2017

No. of 2's & 1's = 1, sol.is 2+1 = 3 = (2^2) - 1
No. of 2's & 1's = 2, sol is 2(3) + 1 =7 =(2^3) - 1
So No. of 2's & 1's =17, sol is 2^(17+1) -1 = (2^18) -1

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