Volume 28
, Issue 1

1992

You have (let's imagine) five maths lessons per week, one each day.

Suppose that $n$ players are engaged in a round robin tennis tournament, that is each player plays each of the other $n-1$ players exactly once.

Interpolation is the process of putting a curve of some sort through a series of points.

There are few problems in 'elementary' mathematics which have not been solved.

The roots of number theory can be traced back over 2,500 years to the time of the Pythagoreans.

Find all positive numbers $x$ which are such that $$\left(1 + \frac{1}{nx}\right)^{-1} > 1 - \frac{1}{n}$$ for every positive integer $n$.

Q.852 If $a_1,a_2,\cdots a_n$ are positive real numbers and $a_1+a_2+\cdots + a_n =1$ prove that $$\sum_{k=1}^n \left(a_k + \frac{1}{a_k}\right)^2 \leq \frac{(n^2+1)^2}{n}.$$

Q.861 each of the numbers in a list $$x_1, x_2, x_3, \cdots , x_n, \cdots$$ is a positive integer written as usual in decimal notation.