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If a, b, c are in A.P. and x, y, z are i...

If a, b, c are in A.P. and x, y, z are in G.P., then prove that :
`x^(b-c).y^(c-a).z^(a-b)=1`

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MAHAVEER PUBLICATION-SERIES-QUESTION BANK
  1. The sum of the series 3+33+333+....+n terms is

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  2. Find the three terms in GP whose sum is 21 and product 64.

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  3. If a, b, c are in A.P. and x, y, z are in G.P., then prove that : x^...

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  4. If a b c are the p^(th), q^(th) and r^(th) terms of an AP then prove t...

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  5. Show that, loge2=1/(1.2)+1/(3.4)+1/(5.6)+.....infty

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  6. Show that, e^x+e^(-x)=2(1+x^2/(2!)+x^4/(4!)+....)

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  7. If, y=x-x^2/2+x^3/3-x^4/4+....oo and (|x|lt1) then x=y+y^2/(a!)+y^3/(b...

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  8. Prove that, 1/(1.2)-1/(2.3)+1/(3.4)-.....=2loge2-1

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  9. Show tha, 1+1/(2!)+1/(4!)+....=1/2(e+1/e)

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  10. Prove that, 1/(2.3)-1/(4.5)+1/(6.7)+.....=1-loge2

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  11. Prove that, 1+(1+2)/(2!)+(1+2+3)/(3!)+(1+2+3+4)/(4!)+....=(3e)/2

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  12. Find the sum of odd integers from 1 to 2001.

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  13. Find 11^(th) term in 09,17,25,33,…..

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  14. How many terms of the A.P. -6,-(11)/(2),-5… are needed to give the sum...

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  15. How many terms of the series : 93+90+87+84+….. Will amount to 975 ?

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  16. Find four arithmetic mean between 3 and 23 ?

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  17. Insert two arithmetic mean between 16 and 22.

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  18. Insert three arithmetic mean (AM) between 1 and 1/16.

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  19. Insert four arithmetic mean (AM) between 4 and 19.

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  20. Insert three arithmetic mean (AM) between 6 and 18.

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