2020 AMC 10A Problems/Problem 8
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 .
We can break this entire sum down into integer bits, in which the sum is , where is the first integer in this bit. We can find that the first sum of every sequence is , which we plug in for the
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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