Final answer:
The value of the given expression is 50.
Step-by-step explanation:
To find the value of the given expression, 100-98+96-94+92-90+..............+8-6+4-2, we can notice that the pattern is alternating between subtracting and adding consecutive even numbers. So, we can rewrite the expression as (100 - 98) + (96 - 94) + (92 - 90) + ............. + (8 - 6) + (4 - 2). Simplifying each pair of numbers gives us 2 + 2 + 2 + ............. + 2 + 2, where the number of pairs is determined by dividing the total number of terms (50) by 2. Hence, we have 2 times the number of pairs, which is 2 * 25 = 50. Therefore, the value of the expression is 50.