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If y is the H.M. between x and z, prove ...

If y is the H.M. between x and z, prove that,
`(1)/(y-x) + (1)/(y-z) = (1)/(x) + (1)/(z)`.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 E (Very Short Answer Type Questions)
  1. What is the value of the H.M. between (a+b) and (a-b) ?

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  2. Insert two HM.s between (1)/(3) and (1)/(24).

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  3. Insert two H.M.s between (-6) and (3)/(13).

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  4. If the G.M. and H.M. of two numbers are 15 and 9 respectively, find th...

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  5. If the A.M. and H.M. of two numbers are 15 and 9(3)/(5) respectively, ...

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  6. If the ratio of G.M. of two numbers to their H.M. is 5 : 4, prove tha...

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  7. If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/...

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  8. If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) ar...

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  9. If a, b, c are in H.P., prove that, a(b+c), b(c+a), c(a+b) are in A...

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  10. If a, b, c are in H.P., prove that, (a)/(a-b) = (a+c)/(a-c)

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  11. If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (a...

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  12. If a^(2), b^(2), c^(2) are in A.P., show that, (b+c), (c+a), (a+b) are...

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  13. If four positive numbers a, b, c and d are in A.P. then prove that abc...

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  14. Prove that, a, b,c are in A.P., G.P. or, H.P. accordingly as (a-b)/(b-...

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  15. If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z ...

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  16. If p, q, r are in A.P., q, r, s are in G.P. and r, s, t are in H.P., p...

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  17. If y is the H.M. between x and z, prove that, (1)/(y-x) + (1)/(y-z) ...

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  18. The harmonic mean of two numbers is 4, their arithmetic mean 'A' and t...

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  19. If the p-th, q-th and the r-th terms of a H.P. be x, y, z respectively...

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  20. A man travels a certain distance with a uniform speed of 5 km/h ad ret...

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