Difference between revisions of "1958 AHSME Problems/Problem 37"

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== Problem ==
 
== 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 expressed as:
+
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 \plus{} (k \plus{} 1)^3\qquad  
+
<math> \textbf{(A)}\ k^3 + (k + 1)^3\qquad  
\textbf{(B)}\ (k \minus{} 1)^3 \plus{} k^3\qquad  
+
\textbf{(B)}\ (k - 1)^3 + k^3\qquad  
\textbf{(C)}\ (k \plus{} 1)^3\qquad \\
+
\textbf{(C)}\ (k + 1)^3\qquad \\
\textbf{(D)}\ (k \plus{} 1)^2\qquad  
+
\textbf{(D)}\ (k + 1)^2\qquad  
\textbf{(E)}\ (2k \plus{} 1)(k \plus{} 1)^2</math>
+
\textbf{(E)}\ (2k + 1)(k + 1)^2</math>
  
 
== Solution ==
 
== Solution ==

Latest revision as of 23:23, 13 March 2015

Problem

The first term of an arithmetic series of consecutive integers is $k^2 + 1$. The sum of $2k + 1$ terms of this series may be expressed as:

$\textbf{(A)}\ k^3 + (k + 1)^3\qquad  \textbf{(B)}\ (k - 1)^3 + k^3\qquad  \textbf{(C)}\ (k + 1)^3\qquad \\ \textbf{(D)}\ (k + 1)^2\qquad  \textbf{(E)}\ (2k + 1)(k + 1)^2$

Solution

$\fbox{}$

See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 36
Followed by
Problem 38
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All AHSME Problems and Solutions

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