Difference between revisions of "1958 AHSME Problems/Problem 37"
(Created page with "== Problem == The first term of an arithmetic series of consecutive integers is <math> k^2 \plus{} 1</math>. The sum of <math> 2k \plus{} 1</math> terms of this series may be exp...") |
Mathgeek2006 (talk | contribs) m (→Problem) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | The first term of an arithmetic series of consecutive integers is <math> k^2 | + | The first term of an arithmetic series of consecutive integers is <math> k^2 + 1</math>. The sum of <math> 2k + 1</math> terms of this series may be expressed as: |
| − | <math> \textbf{(A)}\ k^3 | + | <math> \textbf{(A)}\ k^3 + (k + 1)^3\qquad |
| − | \textbf{(B)}\ (k | + | \textbf{(B)}\ (k - 1)^3 + k^3\qquad |
| − | \textbf{(C)}\ (k | + | \textbf{(C)}\ (k + 1)^3\qquad \\ |
| − | \textbf{(D)}\ (k | + | \textbf{(D)}\ (k + 1)^2\qquad |
| − | \textbf{(E)}\ (2k | + | \textbf{(E)}\ (2k + 1)(k + 1)^2</math> |
== Solution == | == Solution == | ||
Revision as of 23:23, 13 March 2015
Problem
The first term of an arithmetic series of consecutive integers is 
. The sum of 
terms of this series may be expressed as:
Solution
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 36 |
Followed by Problem 38 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
