Sequences and Series
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If a∈(0,2π ), then x2+x+x2+x tan2α is always greater than or equal to
If x,y,z are positive real numbers and x=y+z12−yz. The maximum value of (xyz) equals
The sum of two numbers is 261. An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Find the number of means inserted.
If A1,A2,.....A31 are arithmetic means inserted between the numbers a and b, then find the value of (b−A51b+A51 )−(A1−aA1+a )
A man travels m feet due north at 2 minutes per metre. He returns due south to his starting point at 2 metre per minute. The average rate in miles per hour for the entire trip is:
Insert x arithmetic means between x2 and 1.
If a,b,c are three positive numbers,then the minimum value of the expression bcaab(a+b)+bc(b+c)+ca(c+a)
Find three arithmetic means between 6 and −6.