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If 4a+3b+2c=5 and a>0,b>0,c>0 then the g...

If `4a+3b+2c=5` and `a>0,b>0,c>0` then the greatest value of `a^2b^3c^4` will be ?

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. If a+b+c=abc,a,b and c in R^(+), prove that a+b+c ge 3sqrt(3).

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  2. If a+2b+3c=1 and a>0 , b>0 , c>0 and the greatest value of a^3b^2c is...

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  3. If 4a+3b+2c=5 and a>0,b>0,c>0 then the greatest value of a^2b^3c^4 wil...

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  4. If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432).

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  5. Find the greatest value of the product of three positive numbers if th...

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  6. Find the sum of n terms of the series 1*2*3+2*3*4+3*4*5...........

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  7. Sum to n terms :1*3^2+3*5^2+5*7^2+...

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  8. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+,...

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  9. Sum the series : (1*2)+(1*2+2*3)+(1*2+2*3+3*4)+... to 12 brackets.

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  10. If a1,a2,a3,...,an be in AP whose common difference is d then prove th...

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  11. Find the sum of n terms of the series 1 *2 *3 + 2*4*6 + 3*6*9+...

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  12. Find the sum of n terms of the series 1 + 9 +24 + 46 + 75................

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  13. Find the nth term and sum to n tems of the following series: 3+6+11+18...

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  14. If tn=sum1^n n, find Sn=sum1^n tn.

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  15. Find the sum of n terms of the series 1^2 + 4^2+ 7^2 + .........

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  16. Find the sum of the series 2 + 5 + 14 +41 + 122 +.... up to n terms an...

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  17. The sum to n terms of series 1+(1/2+1/(2^2))+1+(1/2+1/(2^2)+1/(2^3)+1/...

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  18. Find the sum to n terms of the series 5+ 11 + 19 + 29+ 41+ ……

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  19. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

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  20. Find the sum to n terms of the series 1^(2)/(1)+(1^(2)+2^(2))/(1+2)...

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