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If a,b,c,d are in GP then prove that ax^...

If a,b,c,d are in GP then prove that `ax^3+bx^2+cx+d` has a factor `ax^2+c`.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. If a,b,c,d are in GP then prove that a+b,b+c,c+d are in GP.

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  2. If a,b,c,d are in GP then prove that a(b-c)^3=d(a-b)^3.

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  3. If a,b,c,d are in GP then prove that ax^3+bx^2+cx+d has a factor ax^2+...

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  4. Let a1,a2,a3,.....,an be in GP whose common ratio is r. Show that sum(...

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  5. Does there exist a GP containing 27,8 and 12 as threee of its terms ? ...

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  6. Prove that no GP can have three of its terms (not necessarily consecut...

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  7. The product of three numbers in GP is 216 and their sum is 19. Find th...

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  8. Divide 63 into three parts that are in GP and the product of the first...

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  9. The first term of a GP is unity. For what value of the common ratio of...

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  10. For the series sum t(n,) Sn=sum(n=1)^ntn=2tn-1. Is the series geometri...

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  11. If S1, S2, S3 are the sums to n, 2n, 3n terms respectively for a GP th...

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  12. If S1, S2, S3 be respectively the sums of n ,2n ,3n terms of a G.P., t...

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  13. Find sum(n=1)^n un if un=sum(n=0)^n1/2^n.

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  14. STATEMENT -1: (666...n digit)^2+(888... ndigit)=(444....2ndigits) STAT...

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  15. Let a1,a2,a3,.... are in GP. If an>am when n>m and a1+an=66 while a2*a...

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  16. Find the sum of 2n terms of the series whose every even term is ' a ' ...

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  17. If the sum of an infinite G.P is 32 and the some of its first two term...

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  18. If Sn=1+r^n+r^(2n)+r^(3n)+.... to oo and sn=1-r^n+r^(2n)-r^(3n)+... to...

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  19. If x=sum(n=0)^oo a^n, y=sum(n=0)^oo b^n where |a|<1,|b|<1 then prove t...

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  20. If exp. {(sin^2x+sin^4x+sin^6x+…inf.) In2} satisfies the equation x^2-...

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