Invitation to Computer Science 8th Edition

Published by Cengage Learning
ISBN 10: 1337561916
ISBN 13: 978-1-33756-191-4

Chapter 3 - Exercises - Page 139: 1a

Answer

\begin{equation} The\ sum\ is\ 1275 \end{equation} --- By applying the same logic Gauss applied, we notice that for the sum $2+4+\ldots+100$ we can group the numbers from $2$ to $100$ into $25$ pairs of the form $2+100=102$ $4+98=102$ $\cdot$ $\cdot$ $\cdot$ $50+52=102$ The total sum is $25 \cdot 102=2550$ It is easy to notice that 2550 is actually twice the sum we are looking for which is $2550 / 2=1275$ So $2+4+\ldots+100=1275$

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