Difference between revisions of "1964 AHSME Problems/Problem 34"

Revision as of 23:17, 24 July 2019

If $n$ is a multiple of $4$ , the sum $s=1+2i+3i^2+\cdots+(n+1)i^n$ , where $i=\sqrt{-1}$ , equals:

$\textbf{(A) }1+i\qquad\textbf{(B) }\frac{1}{2}(n+2)\qquad\textbf{(C) }\frac{1}{2}(n+2-ni)\qquad$

$\textbf{(D) }\frac{1}{2}[(n+1)(1-i)+2]\qquad \textbf{(E) }\frac{1}{8}(n^2+8-4ni)$

1964 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 33	Followed by Problem 35
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
All AHSME Problems and Solutions

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 <math>\textbf{(D) }\frac{1}{2}[(n+1)(1-i)+2]\qquad \textbf{(E) }\frac{1}{8}(n^2+8-4ni)</math>
+==See Also==
+{{AHSME 40p box|year=1964|num-b=33|num-a=35}}
+[[Category:Introductory Algebra Problems]]
+{{MAA Notice}}