A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- Prove that (2n)^2 where n in N can be expressed as the sum of n terms ...
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- Suppose that a1,a2,....,an,.... is an A.P. Let Sk=a((k-1)n+1)+a((k-1)n...
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- The ratio of the sums of m terms and n terms of an A.P. is m^(2) : n^(...
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- Let r be the common ratio of the GP a1,a2,a3,....,an. Show that 1/(a1^...
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- If S=a+b+c then prove that (S)/(S-a)+(S)/(S-b)+(S)/(S-c) gt (9)/(2) wh...
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- If a, b, x, y are positive natural numbers such that (1)/(x) + (1)/(y)...
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- If ai>0,i=1,2,3,...n and (n-1)s=a1+a2+a3+....+an, prove that a1*a2*a3*...
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- If 2a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greatest value of ...
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- Given the perimeter of a triangle, prove that the triangle of the grea...
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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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- Find the sum of first n terms of the series 0.7 + 0.77 + 0.777 + …..
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- The sum of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+..... upto n...
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- If a1,a2,a3,.....,an are in AP where ai ne kpi for all i, prove that c...
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- Find the sum of the series cot^(-1) 7+cot^(-1)13+cot^(-1)21+cot^(-1)...
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- The coefficient of x^98 in the expression of (x-1)(x-2)......... (x -...
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- If m times the mth term of an AP is equal to n times its nth term, the...
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- Prove that the numbers sqrt2,sqrt3,sqrt5 cannot be three terms (not ne...
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- If a, b and c are three terms of an A.P. such that a !=b, then (b-c)/(...
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- If loglx,logmx,lognx are in AP where x ne 1 and x is positive, prove t...
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- If log3 2, log3 (2^x -5) and log3 (2^x-7/2) are in A.P, determine the ...
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