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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

Page1 / 15

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online