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For the series sum t(n,) Sn=sum(n=1)^ntn...

For the series `sum t_(n,) S_n=sum_(n=1)^nt_n=2t_n-1`. Is the series geometric ? If so, find the sum to `n` terms of the series.

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
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  2. The first term of a GP is unity. For what value of the common ratio of...

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

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

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

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

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

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

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

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

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  11. 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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  12. 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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  13. If exp. {(sin^2x+sin^4x+sin^6x+…inf.) In2} satisfies the equation x^2-...

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  14. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

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  15. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

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  16. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

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  17. If a,b,c are in G.P., then show that : loga, logb, log c are in A.P.

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  18. If a,b,c are in A.P. and x,y,z in G.P., prove that x^(b-c).y^(c-a).z^(...

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  19. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

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  20. 29. If a,b,c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, ...

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