A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- Prove that the product n geometric means between two quantities is equ...
Text Solution
|
- If n arithmetic means xare inserted between 1 and 31 such that the 7^(...
Text Solution
|
- The sum of two numbers is (13)/6dot An even number of arithmetic means...
Text Solution
|
- If a, b, c, d are positive numbers in HP then prove that ad gt bc.
Text Solution
|
- If a, b, c are in AP or GP ot HP where a>0, b>0, c>0 then prove that b...
Text Solution
|
- If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9
Text Solution
|
- If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2.
Text Solution
|
- If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)...
Text Solution
|
- If x>0, y>0, z>0, prove that x^(logy-logz)+y^(logz-logx)+z^(logx-logy)...
Text Solution
|
- If s=a+b+c+d where a, b, c, d are positive unequal numbers then prove ...
Text Solution
|
- If a, b, c are natural numbers, prove that ((a^2+b^2+c^2)/(a+b+c))^(a+...
Text Solution
|
- Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2).
Text Solution
|
- Prove that ((n + 1)/(2))^(n) gt n!
Text Solution
|
- Prove that the product of the first n odd natural numbers cannot excee...
Text Solution
|
- If s be the sum of n positive unequal quantities a, b, c then prove th...
Text Solution
|
- If ai>0, i=1, 2, 3,..., n then prove that a1/a2+a2/a3+a3/a4+...+a(n-1)...
Text Solution
|
- If a ne b and a, b, x, y are positive rational such that x+y=1 then pr...
Text Solution
|
- If x, y, z be three sides of a triangle, prove that xyzge(y+z-x)(z+x-y...
Text Solution
|
- If a,b,c are positive real numbers and sides of a triangle, then prove...
Text Solution
|
- In a triangle ABC, prove that (1+(b-c)/a)^a*(1+(c-a)/b)^b*(1+(a-b)/c)^...
Text Solution
|