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If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b...

If `x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1.` prove that: `1+a b+a^2b^2+oo=(x y)/(x+y-1)`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Sum the following geometric series to infinity: 1/2+1/(3^3)+1/(2^3)+1/...

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  2. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, ...

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  3. If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove...

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  4. If A=1+r^a+r^(2a)+ to oo and B=1+r^b+r^(2b)+oo , prove that r=((A-1)/A...

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  5. Prove that the product n geometric means between two quantities is equ...

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  6. If a ,b ,c ,d are four distinct positive numbers in G.P. then A. a +...

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  7. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n)may be the geo...

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  8. Insert 5 geometric means between 576 and 9.

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  9. Let x be the arithmetic mean and y ,z be tow geometric means between a...

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  10. Find two positive numbers whose difference is 12 an whose A.M. exce...

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  11. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

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  12. If a is the A.M. of b and c and the two geometric means are G1 and G2...

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  13. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

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  14. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

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  15. If a ,b ,c are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+...

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  16. If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prov...

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  17. If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

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  18. If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) ar...

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  19. The sum of three numbers a ,b ,c in A.P. is 18 . If aa n db are eac...

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  20. If a ,b ,c are in G.P., prove that: a(b^2+c^2)=c(a^2+b^2)

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