Summation of series

problem
More polynomial equations

Age

16 to 18

Challenge level

Find relationships between the polynomials a, b and c which are polynomials in n giving the sums of the first n natural numbers, squares and cubes respectively.
problem
Reciprocal triangles

Age

16 to 18

Challenge level

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.
problem
Production equation

Age

16 to 18

Challenge level

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
problem
Googol

Age

16 to 18

Challenge level

Find the smallest value for which a particular sequence is greater than a googol.
problem
Overarch 2

Age

16 to 18

Challenge level

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?
problem
Harmonically

Age

16 to 18

Challenge level

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
problem
Pocket money

Age

11 to 14

Challenge level

Which of these pocket money systems would you rather have?
problem
Picturing square numbers

Age

11 to 14

Challenge level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
problem
Double trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
problem
Picture story

Age

14 to 16

Challenge level

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?