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Let a1,a2,a3,.....,an be in GP whose com...

Let `a_1,a_2,a_3,.....,a_n` be in GP whose common ratio is r. Show that `sum_(k=1)^(n-1) 1/(a_k^2-a_(k+1)^2)=(1-r^(2(n-1)))/(a_1^2*r^(2(n-2))*(1-r^2)^2)`.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
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  3. Let a1,a2,a3,.....,an be in GP whose common ratio is r. Show that sum(...

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

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

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

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

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

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

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

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

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  17. 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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  18. 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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  19. If exp. {(sin^2x+sin^4x+sin^6x+…inf.) In2} satisfies the equation x^2-...

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