Simplify the following expression:

\[ 100 - 99 + 98 - 97 + 96 - 95 + \ldots + 8 - 7 + 6 - 5 + 4 - 3 + 2 - 1 \]

x = 100 − 99 + 98 − 97 + 96 − 95 + ... + 8 − 7 + 6 − 5 + 4 − 3 + 2 − 1 = = 1 + 1 + 1 + ... + 1 + 1 + 1 + 1 = 1 ⋅ n = n an d 2 = 100 − 2 ⋅ ( n − 1 ) ⇒ 2 n = 100 / : 2 ⇒ n = 50 x = 50

Answered by kate200468 | 2024-06-24

100 − 99 + 98 − 97 + 96 − 95 + ... + 8 − 7 + 6 − 5 + 4 − 3 + 2 − 1 = ( 100 − 99 ) + ( 98 − 97 ) + ( 96 − 95 ) + ... + ( 4 − 3 ) + ( 2 − 1 ) = 50 1 + 1 + 1 + ... + 1 ​ ​ = 50 ​

Answered by Anonymous | 2024-06-28

The expression simplifies to 50 by pairing positive and negative terms. Each pair results in 1, and there are 50 pairs total. Thus, the final answer is 50 ​ .
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Answered by Anonymous | 2024-09-27