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2007 iTest Problems/Problem 5

Revision as of 09:49, 16 December 2007 by 1=2 (talk | contribs) (→‎See Also)

Problem

Compute the sum of all twenty-one terms of the geometric series \[1 + 2 + 4 + 8 + \ldots + 1048576\].

$\mathrm{(A)}\,2097149\quad\mathrm{(B)}\,2097151\quad\mathrm{(C)}\,2097153\quad\mathrm{(D)}\,2097157\quad\mathrm{(E)}\,2097161$

Solution

Those are powers of 2. So it would make sense to multiply the series by 2:

$x=1 + 2 + 4 + 8 + \ldots + 1048576$

$2x=2 + 4 + 8 + \ldots + 1048576 + 2097152$

Subtracting,

$x=2097152-1=2097151 \Rightarrow \mathrm {(B)}$

See Also

2007 iTest (Problems, Answer Key)
Preceded by:
First question 		Followed by:
Problem 6
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