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If S=1/(1xx3xx5)+1/(3xx5xx7)+1/(5xx7xx9)...

If `S=1/(1xx3xx5)+1/(3xx5xx7)+1/(5xx7xx9)+ddot` to infinity, then find the value of `[36 S]` , where [.] represents the greatest integer function.

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
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  2. Find the sum of the series 1^2+3^2+5^2+ ton terms.

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  3. If S=1/(1xx3xx5)+1/(3xx5xx7)+1/(5xx7xx9)+ddot to infinity, then find t...

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  4. If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equ...

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  5. Let Tr denote the rth term of a G.P. for r=1,2,3, If for some positive...

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  6. Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

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  7. Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c

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  9. If S=a1+a2+......+an,ai in R^+ for i=1 to n, then prove that S/(S-a1)...

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  11. If a ,b >0 such that a^3+b^3=2, then show that a+blt=2.

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  12. Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

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  13. In a triangle A B C prove that a//(a+c)+b//(c+a)+c//(a+b)<2

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  14. Find the least value of secA+secB+secC in an acute angled triangle.

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  15. Prove that [(n+1)//2]^n >(n !)dot

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  17. If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...

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  18. If (log)(10)(x^3+y^3)-(log)(10)(x^2+y^2-x y)lt=2, and x ,y are positiv...

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  19. If (log)2(a+b)+(log)2(c+d)geq4. Then find the minimum value of the exp...

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  20. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

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