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

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

Summing Squares

Age

14 to 16

Challenge level

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
problem

Vanishing Point

Age

14 to 18

Challenge level

How can visual patterns be used to prove sums of series?
interactivity

Proof Sorter - Geometric Sequence

Age

16 to 18

Challenge level

Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?
problem

Degree Ceremony

Age

16 to 18

Challenge level

Can you find the sum of the squared sine values?
problem

Summats Clear

Age

16 to 18

Challenge level

Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
problem

Seriesly

Age

16 to 18

Challenge level

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!