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1 10.2: Series Definitions: Infinite Series: N th Partial Sum: Convergent Series: Divergent Series: Special (Summable) Kinds of Series: Geometric Series: Find the values of r for which ∞ X arn−1 is convergent and find the sum. n=1 1 Telescoping Series: Find the sum of ∞ X 1 n=1 n − 1 n+2 Properties of Convergent Series: If ∞ X an and n=0 i) ∞ X bn are convergent, then: n=0 ii) iii) Tests for Convergence of Series: (continued through 10.4) I. The Test for Divergence (or Divergence Test): ∞ X n+3 2n + 1 n=0 2 . On Beyond Average: A window consists of two parallel panes of tinted glass with a small air space between the panes. Whenever light hits either pane of glass on either side, 1/3 of the light passes through the pane and 2/3 is reflected back. If a light shines on one side of the window, what fraction of the light passes through the window? The N th partial sum of a series is given by sN = the series is divergent. N +1 . Find the sum of the series or explain why 2N + 3 Prove the converse of the Test for Divergence is false by showing that 1 → 0). n 3 ∞ X 1 diverges (even though n n=1