MTH 1322 – Calculus II Homework 12 – Summing an Infinite Series 1. Write the series in Σ-notation and evaluate its sum. (c) 1 2 − 1 6 + 1 18 − 1 54 + 1 162 − 1 486 + · · · Hint : This is a geometric...

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MTH 1322 – Calculus II Homework 12 – Summing an Infinite Series 1. Write the series in Σ-notation and evaluate its sum. (c) 1 2 − 1 6 + 1 18 − 1 54 + 1 162 − 1 486 + · · · Hint : This is a geometric series. (d) 1 1 · 3 + 1 3 · 5 + 1 5 · 7 + 1 7 · 9 + 1 9 · 11 + · · · Hint : This is a telescoping series. 2. Determine whether the series converges or diverges. (d) ∞∑ n=2 1 n √ 3 4. Use a geometric series to show that 0.4999 . . . = 1 2 .