2020 AMC 10 A

Solution 1: Split the even numbers and the odd numbers apart. If we group every even numbers together and add them, we get a total of . Summing the odd numbers is equivalent to summing the first 100 odd numbers, which is equal to . Adding these two, we obtain the answer of (B) 9900

Solution 2 (bashy): 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 50 bits in the entire sequence is , so then we can plug it into the first term of every sequence equation we got above , and so the sum of every bit is , and we only found the value of , the sum of the sequence