Summation of series

problem

More Polynomial Equations

Age

16 to 18

Challenge level

2 out of 3

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

2 out of 3

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

2 out of 3

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

3 out of 3

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

2 out of 3

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

2 out of 3

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

Proof Sorter - Geometric Sequence

Age

16 to 18

Challenge level

1 out of 3

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

1 out of 3

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

Summats Clear

Age

16 to 18

Challenge level

1 out of 3

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

1 out of 3

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