9.4 part 4.ppt worked
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1) A geometric series is the expression of the sum of terms in a geometric sequence. The sum of a finite geometric series can be calculated using the formula Sn = a(1 - r^n)/(1 - r) where a is the first term, r is the common ratio, and n is the number of terms. 2) Geometric series converge when the absolute value of the common ratio r is less than 1, and diverge when the absolute value of r is greater than 1. 3) The homework assignment includes evaluating example geometric series, determining whether other series converge or diverge, and completing a worksheet to review for a test on geometric series.
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9.4 part 4.ppt worked
- 3. Geometric Series A geometric series is the expression of the sum of the terms of a geometric sequence. Sum of a finite Geometric Series: r ra S n n − − = 1 )1(1
- 4. Evaluate the series 1. 3 + 6 + 12 + 24 + 48 + 96 2. - 45 + 135 – 405 + 1215 – 3645 3. 81 1 27 1 9 1 3 1 +++
- 5. Convergence: When |r| < 1, the series converges Gets closer and closer to the sum When |r| > 1, the series diverges Approaches no limit
- 6. Determine convergence or divergence: 1. 2. 3. 4. ... 9 1 3 1 1 −+− ... 25 1 5 1 1 +++ ∑ ∞ = − 1 1 )2(5 n n 1684 ++
- 7. Sum of Infinite Geometric Series 1. 2. ... 8 1 4 1 2 1 1 ++++ r a S − = 1 1 ... 8 3 4 3 2 3 3 +−+−
- 8. Homework WORKSHEET Get a jump on your review for your test…it’s TOMORROW!