2018 AMC 12B Problems/Problem 9

Problem

What is $\sum^{100}_{i=1} \sum^{100}_{j=1} (i+j) ?$

$\textbf{(A) }100,100 \qquad \textbf{(B) }500,500\qquad \textbf{(C) }505,000 \qquad \textbf{(D) }1,001,00 \qquad \textbf{(E) }1,010,000 \qquad$

$\sum^{100}_{i=1} \sum^{100}_{j=1} (i+j) = \sum^{100}_{i=1} 100i+5050 = 100 \cdot 5050 + 5050 \cdot 100 = \boxed{1,010,000}$ (Vfire)

2018 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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All AMC 12 Problems and Solutions