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If a, b and c are in G.P. then prove tha...

If a, b and c are in G.P. then prove that 1 a 2 - b 2 + 1 b 2 = 1 b 2 - c 2 . 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find the sum 2+5+10+17+26+. . . .

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  2. Find the sum up to 20 terms. 1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+....

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  3. If a, b and c are in G.P. then prove that <math xmlns="http://www.w3...

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  4. Find the value of (32).(32)^(1//6).(32)^(1//36) ......... oo.

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  5. Find the sum of the series 1^2+3^2+5^2+ ton terms.

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

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

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

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  9. 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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  10. If y z+z x+x y=12 , and x , y , z are positive values, find the great...

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

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  12. If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)+...+2^(n m-m)> n^(1-m)...

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

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

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

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

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

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  18. If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...

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

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  20. 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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