∞ 2. Letan be a positive series. Note that either an converges (so partial sums converge to a n=m limit), or the partial

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2 Letan Be A Positive Series Note That Either An Converges So Partial Sums Converge To A N M Limit Or The Partial 1 (36.29 KiB) Viewed 80 times

∞ 2. Letan be a positive series. Note that either an converges (so partial sums converge to a n=m limit), or the partial sums s; approach oo as j grows without bound (and we associate 80 COMPARISON TEST: Letan and b, be positive series. Σ, and Σ n=m n=m i. If a, converges and 0 ≤ bn San for all n, then b, converges. TLM ∞ 00 (2) Σ ii. If an diverges and 0 <an<bn for all n, then n=m nom 7=1 n2n n=2 n=m Use the Comparison Test, and the Ratio Test or Root Test where applicable, to determine whether each of the following series converges, or diverges. nom 00 (c) Σ 7=1 b, diverges. n=m 1 (2n + 1)(n+1) an with co). (Hint: Use Exercise 1 above.)