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If 1/a ,1/b ,1/c are in A.P. prove that:...

If `1/a ,1/b ,1/c` are in A.P. prove that: `(b+c)/a ,(c+a)/b ,(a+b)/c` are in A.P.

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. The sum of n terms of two arithmetic progressions are in the ratio 5n+...

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  2. If 2/3, k ,5/8 are in A.P., find the value of kdot

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  3. If 1/a ,1/b ,1/c are in A.P. prove that: (b+c)/a ,(c+a)/b ,(a+b)/c are...

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  4. If a, b, c are in A.P., prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" a...

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  5. If a, b, c are in A.P, then show that: b+c-a ,\ c+a-b ,\ a+b-c are in ...

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  6. If a, b, c are in A.P, then show that: \ b c-a^2,\ c a-b^2,\ a b-c^2 a...

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  7. If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are als...

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  8. If (b+c)/a ,(c+a)/b ,(a+b)/c are in A.P., prove that : b c ,\ c a ,\ a...

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  9. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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  10. Insert 3 arithmetic means between 3 and 19.

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  11. For what value of n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n) is the arithmeti...

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  12. Between 1 and 31 are inserted m arithmetic mean so that the ratio of t...

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  13. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  14. Find the A.M. between: 7 and 13

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  15. Find the A.M. between: 12\ a n d-8

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  16. Find the A.M. between: (x-y)a n d\ (x+y)

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  17. Insert 4 A.M.s between 4 and 19.

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  18. Insert 7 A.M.s between 2 and 17.

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  19. Insert six A.M.s between 15 and -13.

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  20. There are n A.M.s between 3 and 17. The ratio of the last mean to the ...

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