A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- If s=a+b+c+d where a, b, c, d are positive unequal numbers then prove ...
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- If a, b, c are natural numbers, prove that ((a^2+b^2+c^2)/(a+b+c))^(a+...
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- Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2).
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- Prove that ((n + 1)/(2))^(n) gt n!
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- Prove that the product of the first n odd natural numbers cannot excee...
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- If s be the sum of n positive unequal quantities a, b, c then prove th...
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- If ai>0, i=1, 2, 3,..., n then prove that a1/a2+a2/a3+a3/a4+...+a(n-1)...
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- If a ne b and a, b, x, y are positive rational such that x+y=1 then pr...
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- If x, y, z be three sides of a triangle, prove that xyzge(y+z-x)(z+x-y...
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- If a,b,c are positive real numbers and sides of a triangle, then prove...
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- In a triangle ABC, prove that (1+(b-c)/a)^a*(1+(c-a)/b)^b*(1+(a-b)/c)^...
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- If a+b+c=abc,a,b and c in R^(+), prove that a+b+c ge 3sqrt(3).
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- 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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- 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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