In this system one degree is divided equally into

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Unformatted text preview: = n−1 2n−1 2n−1 , , n≥1 n≥1 (g) geometric, r = 10 (h) neither n , n≥1 3n−1 1 an = n2 , n ≥ 1 (−1)n−1 x2n−1 , n≥ 2n−1 10n −1 10n , (d) an = (g) an = (e) (h) an = (n + 2)3 , n ≥ 1 (f) 1 (i) an = n≥1 1+(−1)n−1 , 2 n≥1 562 9.2 Sequences and the Binomial Theorem Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a definition, which, while intimidating, is meant to make our lives easier. Definition 9.3. Summation Notation: Given a sequence {an }∞ k and numbers m and p n= satisfying k ≤ m ≤ p, the summation from m to p of the sequence {an } is written p an = am + am+1 + . . . + ap n=m The variable n is called the index of summation. The number m is called the lower limit of summation while the number p is called the upper limit of summation. In English, Definition 9.3 is simply defining a short-hand notation for adding up the terms of the sequence {an }∞ k from am through ap . The symbol Σ is the capi...
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