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Method and examples
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Geometric Progression |
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Problem 21 of 23 |
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21. For geometric progression, find + ... n terms where x = and n = .
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Solution
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Solution provided by AtoZmath.com
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This is demo example. Please click on Find button and solution will be displayed in Solution tab (step by step)
| Geometric Progression |
21. For geometric progression, find `1 + 1/sqrt(2) + 1/2 + 1/(2*sqrt(2)) + ... 10` terms ( For geometric progression, find `1 + 1/sqrt(x) + 1/x + 1/(x*sqrt(x)) + ... n` terms where x = 2 and n = 10 . )
Here `a = 1, r = 1 / sqrt(2), n = 10`
We know that, `S_n = a * (1 - r^n)/(1 - r)`
`:. S_10 = 1 × (1 - (1 / sqrt(2))^10) / (1 - 1 / sqrt(2))`
`= 1 × (1 - (1 / 2)^5) / ((sqrt(2) - 1) / sqrt(2))`
`= sqrt(2) × 1 × (1 - 1 / 32) / (sqrt(2) - 1) `
`= sqrt(2) × 1 × ((32 - 1) / 32) / (sqrt(2) - 1) × (sqrt(2) + 1) / (sqrt(2) + 1)`
`= sqrt(2) × 1 × (31/32) / (2 - 1) × (sqrt(2) + 1)`
`= (31/32) × sqrt(2) × (sqrt(2) + 1)`
`= (31/32) × (2 + sqrt(2))`
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