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If a be the first term, b be the nth ter...

If `a` be the first term, `b` be the `nth` term and P be the product of `n` terms of a GP then prove that `P^2=(ab)^n`.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. In a GP, t(p+q)=a and t(p-q)=b. Prove that tp=sqrt(ab).

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  2. If the pth, qth and rth terms of a G.P. are a,b and c, respectively. ...

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  3. If a be the first term, b be the nth term and P be the product of n te...

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  4. If a,b,c are in GP, prove that (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2).

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

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  6. If a,b,c,d are in GP then prove that a+b,b+c,c+d are in GP.

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

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

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

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

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

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

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

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

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

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

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

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

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

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