AlgebraDifficulty 4.2AIMEFind the answerUnited States
Problem:
Sindy writes down the positive integers less than 200 in increasing order, but skips the multiples of 10. She then alternately places + and − signs before each of the integers, yielding an expression +1−2+3−4+5−6+7−8+9−11+12−⋯−199. What is the value of the resulting expression?
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
Solution:
Group the numbers into (1−2+3−4+…+18−19)+(21−22+…+38−39)+…+(181−182+…+198−199). We can easily show that each group is equal to −10, and so the answer is −100.
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Source: MathNet,
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