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If x,y,z are in GP, then prove that logx...

If x,y,z are in GP, then prove that logx,logy,logz are in AP.

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If x,y,z are in GP than we can write `y/x=z/y`
Taking logarithm on both side we have, `logy/x = log z/y implies logy-logx = logz-logy`
which show that logx, logy,logz are in AP.
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MAHAVEER PUBLICATION-SERIES-QUESTION BANK
  1. Find k if 2k+1,k,3k+2 are in GP.

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  2. Find8^(th) term of the GP 1,4,16,…..

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  3. If x,y,z are in GP, then prove that logx,logy,logz are in AP.

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  4. If 3^(rd) term of an arithmetic progression is and term is 18 and 17^(...

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  5. The sum of the series 3+33+333+....+n terms is

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Find four arithmetic mean between 3 and 23 ?

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