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Geometric series
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Geometric series
A geometric series is the sum of a finite number of terms in a geometric sequence. Just like the arithmetic series, we also have geometric series formulas to help us with that.
Related Concepts: Pascal's triangle, Binomial theorem, Introduction to infinite series, Convergence & divergence of geometric series
Lessons
The sum of n terms of a geometric series:
Sn=r−1t1(rn−1)=r−1r⋅tn−t1
- 1.Geometric series formula:sn=r−1t1(rn−1)
Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … . - 2.Geometric series formula: sn=r−1r⋅tn−t1
Determine the sum of the geometric series: 8 + 2 + 21 + …. + 5121 . - 3.A tennis ball is dropped from the top of a building 15 m high. Each time the ball hits the ground, it bounces back to only 60% of its previous height. What is the total vertical distance the ball has travelled when it hits the ground for the fifth time?