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Express each of the following recurring ...

Express each of the following recurring decimals in the form of an infinite geometric series and obtain their values in the form of rational numbers :
`0.3`

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The correct Answer is:
`(1)/(3)`
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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 D (Very Short Answer Type Questions)
  1. Find the sum of each of the following infinite geometric series, if it...

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  2. Find the sum of each of the following infinite geometric series, if it...

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  3. Express each of the following recurring decimals in the form of an inf...

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  4. Express each of the following recurring decimals in the form of an inf...

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  5. Express each of the following recurring decimals in the form of an inf...

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  6. Express each of the following recurring decimals in the form of an inf...

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  7. Express 0.overset(.)4 as an infinite geometric series and hence prove ...

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  8. The sum of an infinite geometric series is (1)/(3) and its first terms...

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  9. The sum of an infinite geometric series is 6 and the sum of its first ...

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  10. In a G.P. the sum of infinite terms is 15, the sum of the squares of t...

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  11. Two infinite geometric series starts from the same number. If the comm...

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  12. The distance passed over by a certain pendulum bob in succeeding swing...

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  13. In an infinite G.P., each term is equal to three times the sum of all ...

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  14. If x = a + (a)/(r ) + (a)/(r^(2))+…oo (-1 lt (1)/(r ) lt 1), y = b -...

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  15. If |a| lt 1, |b| lt 1, then show that a(a+b) + a^(2) (a^(2) + b^(2))...

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  16. If, for real numbers a, b, c, r with |r| gt 1, x = a + (a)/(r ) + (a)/...

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  17. If for two reals a, b, with |a| gt 1, |b| gt 1, x = 1 + (1)/(a) + (1)/...

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  18. For a real number 'a' with |a| lt 1, if x = a - a^(3) + a^(5)-…, y = 1...

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  19. For a real number a with 0 lt a lt (1)/(2), if b = 1 - a + a^(2) - a^(...

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  20. If, for 0 lt a lt (1)/(2), the sum of series a+a^(2) + a^(3)+… is b, t...

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