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If A and G be the A.M. and G.M. of two n...

If A and G be the A.M. and G.M. of two numbers a and b and `A:G=m:n`,then prove that- `a:b=m+sqrt(m^2-n^2) :m-sqrt(m^2-n^2)`

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KALYANI PUBLICATION-PROGRESSION-EXERCISE
  1. Prove that the product of n G.M.’s between a and b is (ab)^(n/2)

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  2. The A.M. of two positive numbers a and b is twice their G.M. Prove tha...

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  3. If A and G be the A.M. and G.M. of two numbers a and b and A:G=m:n,the...

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  4. Find the sum of the following series 1 + 2 + 4….. to tenth term.

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  5. Find the sum of the following series 1 + 3 + 9….... to tenth term

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  6. Find the sum of the following series 128 + 64 + 32... to tenth term...

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  7. Find the sum of the following series:1-3+9-27+…. to the 9th term.

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  8. Find the sum of the following series:1/sqrt(2)-1+sqrt(2)… to the 10th ...

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  9. Find the sum of the following series 1+1/3+1/3^2….to tenth term.

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  10. Find the sum of the following series:2+1+1/2+1/(2^2)….to the nth term.

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  11. Find the sum of the following series (x+y)/(x-y)+1+(x-y)/(x+y)+…. to...

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  12. Find the sum of the following series (a-x)+(a^2-x^2)+(a^3-x^3)+….. T...

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  13. Find the number of terms if- 1+2+4+….=32767

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  14. Find the number of terms if- 64+32+16+….=127(1/2).

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  15. Find the number of terms if- 3-6+12-24+….=-1023.

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  16. Find the sum of first n terms of the following 1+11+111+1111+….

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  17. Find the sum of first n terms of the following 5+55+555+….

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  18. Find the sum of first n terms of the following 3+33+333+…..

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  19. Find the sum of first n terms of the following .7+.77+.777+…..

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  20. Find the sum of first n term of the following series 4+0.4+0.44+….

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