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1962 AHSME Problems/Problem 32

Revision as of 22:23, 9 November 2013 by Fadebekun (talk | contribs) (Created page with "==Problem== If <math>x_{k+1} = x_k + \frac12 for k=1, 2, \dots, n-1</math> and <math>x_1=1</math>, find <math>x_1 + x_2 + \dots + x_n</math>. <math> \textbf{(A)}\ \frac{n+1}{2}...")

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Problem

If $x_{k+1} = x_k + \frac12 for k=1, 2, \dots, n-1$ and $x_1=1$ , find $x_1 + x_2 + \dots + x_n$ .

$\textbf{(A)}\ \frac{n+1}{2}\qquad\textbf{(B)}\ \frac{n+3}{2}\qquad\textbf{(C)}\ \frac{n^2-1}{2}\qquad\textbf{(D)}\ \frac{n^2+n}{4}\qquad\textbf{(E)}\ \frac{n^2+3n}{4}$

Solution

"Unsolved"

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