Difference between revisions of "2007 iTest Problems/Problem 5"
(New page: ==Problem== Compute the sum of all twenty-one terms of the geometric series <cmath>1 + 2 + 4 + 8 + \ldots + 1048576</cmath>. <math>\mathrm{(A)}\,2097149\quad\mathrm{(B)}\,2097151\quad\mat...) |
(category) |
||
| (4 intermediate revisions by one other user not shown) | |||
| Line 17: | Line 17: | ||
==See Also== | ==See Also== | ||
| + | {{iTest box|year=2007|num-b=4|num-a=6}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 19:46, 14 January 2008
Problem
Compute the sum of all twenty-one terms of the geometric series
![\[1 + 2 + 4 + 8 + \ldots + 1048576\]](http://latex.artofproblemsolving.com/c/c/1/cc1b6f284c8465d2e1aa0af729878c3a9ab4fdbf.png)
.
Solution
Those are powers of 2. So it would make sense to multiply the series by 2:
Subtracting,
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 4 |
Followed by: Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
