A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- If x,y and z are in A.P ax,by and cz in G.P and a, b, c in H.P then p...
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- a, b, x are in AP, a, b, y are in GP and a, b, z are in HP, then prove...
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- If a , b , c , are in A P ,a^2,b^2,c^2 are in HP, then prove that eith...
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- If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove tha...
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- If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...
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- The values of xyz is 15/2 or 18/5 according as the series a, x, y, z, ...
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- 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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