Problem
$\sum_{i=1}^{10}\left[1+(-1)^{i}\right]=$
Solution
Step 1 ：The sum is over the range from 1 to 10. For each i, the term is \(1+(-1)^{i}\). When i is even, \((-1)^{i}\) is 1, and when i is odd, \((-1)^{i}\) is -1. So, the term is 2 for even i and 0 for odd i.
Step 2 ：Since half of the numbers from 1 to 10 are even, the sum should be \(2*5=10\).
Step 3 ：Final Answer: \(\boxed{10}\)
