Final answer:
The value of the sum 100-98+96-94+...+8-6+4-2 is found by recognizing that each number pair subtracts to give -2. There are 50 such pairs between 2 and 100, which means the sum is 50 * 2 = 100.
Step-by-step explanation:
To find the value of the alternating sum 100-98+96-94+...+8-6+4-2, we observe that each pair of numbers is a sum that subtracts 2 from an even number, resulting in a series of negative twos. To calculate the sum, we pair the numbers two at a time:
- (100 - 98) = 2
- (96 - 94) = 2
- (92 - 90) = 2
- ...
- (8 - 6) = 2
- (4 - 2) = 2
Since there are 50 even numbers between 2 and 100, there will be 50 pairs. Multiplying 50 by the result of each pair, which is 2, we get the final sum:
50 x 2 = 100.
Therefore, the value of the sum is 100.