What is the value of the following expression? &2(2(2(2(2(2+1)+1) & +1)+1)+1)+1

2017 AMC 10A Problem 1

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What is the value of the following expression?

\begin{aligned} &2(2(2(2(2(2+1)+1)\\ &\qquad{}+1)+1)+1)+1 \end{aligned}

70

97

127

159

729

Work from the innermost parentheses outward

Notice the intermediate values are one less than powers of two

Starting with the innermost

2+1,

each new layer doubles the current value and adds

1.

The successive values are

3,7,15,31,63,127.

Thus, C is the correct answer.