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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- In a A.P & an H.P have the same first term, the same last term & the s...
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- l, m, n are three numbers in G.P., a is the first term of an A.P., who...
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- Three unequal numbers are in HP and their squares are in AP. Show that...
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- Insert 12 arithmetic means between -3.5 and -42.5.
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- Insert 6 geometric means between 27 and 1/(81)dot
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- Find the 5th harmonic mean when n harmonic means are inserted between ...
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- If n A.Ms are inserted between two numbers, prove that the sum of the ...
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- Prove that the product n geometric means between two quantities is equ...
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- If n arithmetic means xare inserted between 1 and 31 such that the 7^(...
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- The sum of two numbers is (13)/6dot An even number of arithmetic means...
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- If a, b, c, d are positive numbers in HP then prove that ad gt bc.
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- If a, b, c are in AP or GP ot HP where a>0, b>0, c>0 then prove that b...
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- If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9
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- If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2.
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- If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)...
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- If x>0, y>0, z>0, prove that x^(logy-logz)+y^(logz-logx)+z^(logx-logy)...
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- 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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