UPSC > CSAT Preparation > Geometric, Mixed & Alternate Series
Geometric, Mixed & Alternate Series Video Lecture - CSAT Preparation - UPSC
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197 videos|151 docs|200 tests
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FAQs on Geometric, Mixed & Alternate Series Video Lecture - CSAT Preparation - UPSC
| 1. What is a geometric series? |  |
Ans. A geometric series is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant. For example, 2, 4, 8, 16 is a geometric series with a common ratio of 2.
| 2. How can I find the sum of a geometric series? | |
Ans. The sum of a geometric series can be found using the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. Make sure that the absolute value of r is less than 1 for the formula to be valid.
| 3. What is a mixed series? | |
Ans. A mixed series is a sequence of numbers that alternates between two different patterns. For example, 1, 3, 2, 6, 4, 12 is a mixed series where the odd terms follow a geometric pattern (multiply by 3) and the even terms follow a different pattern (multiply by 2).
| 4. How can I find the sum of a mixed series? | |
Ans. Finding the sum of a mixed series can be more challenging than a regular geometric series. You need to separately find the sums of the two different patterns and then add them together. You can use the formulas for geometric series or use algebraic manipulations to find the sums.
| 5. What is an alternate series? | |
Ans. An alternate series is a sequence of numbers where the terms alternate between positive and negative. For example, 1, -2, 3, -4, 5, -6 is an alternate series. The signs of the terms can follow a specific pattern or be randomly assigned.
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Video Description: Geometric, Mixed & Alternate Series for UPSC 2023 is part of CSAT Preparation preparation.
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197 videos|151 docs|200 tests
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Timeline
| 00:00 | Introduction |
| 00:54 | Geometric Series |
| 04:58 | Mixed Series |
| 07:51 | Arithmetico-Geometric |
| 09:31 | Alternate Series |
| 11:58 | Question 1 |
| 14:00 | Question 2 |
| 15:46 | Question 3 |
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