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Prove that for every positive integer n ...

Prove that for every positive integer n the following inequality holds true: `(1)/(9)+(1)/(25)+…..+(1)/((2n+1)^2)lt(1)/(4)`.

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MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced
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  3. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  4. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  6. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  7. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  8. A straight line through the vertex P of a triangle PQR intersects the ...

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  9. Suppose four distinct positive numbers a1,a2,a3,a4 are in G.P. Let b1=...

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  10. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

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  11. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

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  12. Let a(1),a(2),a(3),"........."a(11) be real numbers satisfying a(1)=15...

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  13. The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^...

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  14. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

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  15. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

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  16. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  17. Let an denote the number of all n-digit positive integers formed by th...

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  18. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

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  21. Suppose that all the terms of an arithmetic progression (A.P.) are nat...

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