Number sense puzzles (contest style)

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Learn it Look for shortcuts: pair numbers to add a long list, find the repeating cycle of ones digits, and use the middle number for consecutive sums.

Example: Find $1 + 2 + 3 + \dots + 100$.

Pair the first and last: $1 + 100 = 101$, $2 + 99 = 101$, …
There are 50 pairs.
$50 \times 101 = 5{,}050$.

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