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Re: S is a sequence such that Sn = (–1)n for each integer n ≥ 1.
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12 Aug 2018, 06:58
Explanation
Adding 20 individual terms would take quite a long time. Look for a pattern. The first several terms in \(S_n = (-1)^n\), where n ≥ 1:
\(S_1 = (-1)1 = -1\)
\(S_2 = (-1)2 = 1\)
\(S_3 = (-1)3 = -1\)
\(S_4 = (-1)4 = 1\)
The terms alternate –1, 1, –1, 1, and so on. If the terms are added, every pair of –1 and 1 will add to zero; in other words, for an even number of terms, the sum will be zero. Since 20 is an even number, so the first 20 terms sum to zero.