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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- 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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- If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432).
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- Find the greatest value of the product of three positive numbers if th...
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- Find the sum of n terms of the series 1*2*3+2*3*4+3*4*5...........
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- Sum to n terms :1*3^2+3*5^2+5*7^2+...
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- Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+,...
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- Sum the series : (1*2)+(1*2+2*3)+(1*2+2*3+3*4)+... to 12 brackets.
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- If a1,a2,a3,...,an be in AP whose common difference is d then prove th...
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- Find the sum of n terms of the series 1 *2 *3 + 2*4*6 + 3*6*9+...
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- Find the sum of n terms of the series 1 + 9 +24 + 46 + 75................
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- Find the nth term and sum to n tems of the following series: 3+6+11+18...
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- If tn=sum1^n n, find Sn=sum1^n tn.
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- Find the sum of n terms of the series 1^2 + 4^2+ 7^2 + .........
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- Find the sum of the series 2 + 5 + 14 +41 + 122 +.... up to n terms an...
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- 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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- Find the sum to n terms of the series 5+ 11 + 19 + 29+ 41+ ……
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- The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...
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- Find the sum to n terms of the series 1^(2)/(1)+(1^(2)+2^(2))/(1+2)...
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- Find sum n^3 from n=1 to n=100.
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- Evaluate sum(n=1)^n {sum(n=1)^n (2^n+3n)}.
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