Difference between revisions of "2020 AMC 10A Problems/Problem 8"
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<math>\textbf{(A) } 9,800 \qquad \textbf{(B) } 9,900 \qquad \textbf{(C) } 10,000 \qquad \textbf{(D) } 10,100 \qquad \textbf{(E) } 10,200</math> | <math>\textbf{(A) } 9,800 \qquad \textbf{(B) } 9,900 \qquad \textbf{(C) } 10,000 \qquad \textbf{(D) } 10,100 \qquad \textbf{(E) } 10,200</math> | ||
| − | == | + | == Solution == |
| + | |||
| + | Split the even numbers and the odd numbers apart. If we group every 2 even numbers together and add them, we get a total of <math>50\cdot (-2)=-100</math>. Summing the odd numbers is equivalent is equivalent to summing the first 100 odd numbers, which is equal to <math>100^2=10000</math>. Adding these two, we obtain the answer of <math>9900</math>. | ||
==See Also== | ==See Also== | ||
Revision as of 21:16, 31 January 2020
Problem
What is the value of
Solution
Split the even numbers and the odd numbers apart. If we group every 2 even numbers together and add them, we get a total of 
. Summing the odd numbers is equivalent is equivalent to summing the first 100 odd numbers, which is equal to 
. Adding these two, we obtain the answer of 
.
See Also
| 2020 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
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