# sn8_1 - Math 1432 Notes – session 8 11.1 Infinite Series...

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Unformatted text preview: Math 1432 Notes – session 8 11.1 Infinite Series The infinite series: ∑ ∞ = k k a What this means – ∑ ∞ = k k a = If terms 0, then An infinite series will converge IF the sequence (list) of PARTIAL SUMS converges. Ex: 1 2 k k ∞ = ∑ If the sequence of partial sums {s n } converges to a finite limit L we write L a k k = ∑ ∞ = and say that ∑ ∞ = k k a converges to L and L is the sum of the series. Geometric Series: ,... , , , 1 3 2 x x x is a geometric series. We write: ∑ ∞ = k k x If 1 < x then x x k k- = ∑ ∞ = 1 1 If 1 ≥ x then ∑ ∞ = k k x diverges Note: ( 29 r r r N N n n-- = + = ∑ 1 1 1 for any r Ex: 1. 5 3 k k ∞ = ∑ 2. 7 9 k k ∞ = ∑ 3. 3 4 k k ∞ = - ∑ 4. ( 29 2 k k ∞ =- ∑ General Properties: If ∑ ∞ = k k a converges and ∑ ∞ = k k b converges, then ( 29 ∑ ∞ = + k k k b a converges If ∑ ∞ = k k a converges, then ∑ ∞ = k k a α converges ( = k k a α ∞ = ∑ ) Thm – If ∑ ∞ = k k a converges then → k a as ∞ → k ....
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sn8_1 - Math 1432 Notes – session 8 11.1 Infinite Series...

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