Search by Topic

Resources tagged with Summation of series similar to Production Equation:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 26 results

Broad Topics > Advanced Algebra > Summation of series

problem icon

Production Equation

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Overarch 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level: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 icon

Degree Ceremony

Stage: 5 Challenge Level: Challenge Level:1

What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?

problem icon

Sum the Series

Stage: 5

This article by Alex Goodwin, age 18 of Madras College, St Andrews describes how to find the sum of 1 + 22 + 333 + 4444 + ... to n terms.

problem icon

Harmonically

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Seriesly

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Weekly Challenge 36: Seriesly

Stage: 5 Short Challenge Level: Challenge Level:1

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

problem icon

Double Trouble

Stage: 4 Challenge Level: Challenge Level:1

Simple additions can lead to intriguing results...

problem icon

Reciprocal Triangles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

The Kth Sum of N Numbers

Stage: 5

Yatir from Israel describes his method for summing a series of triangle numbers.

problem icon

2^n -n Numbers

Stage: 5

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.

problem icon

Weekly Challenge 34: Googol

Stage: 5 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Speedy Summations

Stage: 5 Challenge Level: Challenge Level:1

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

problem icon

Slick Summing

Stage: 4 Challenge Level: Challenge Level:1

Watch the video to see how Charlie works out the sum. Can you adapt his method?

problem icon

Sums of Powers - A Festive Story

Stage: 3 and 4

A story for students about adding powers of integers - with a festive twist.

problem icon

Summing Geometric Progressions

Stage: 4 and 5 Challenge Level: Challenge Level:1

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

problem icon

More Polynomial Equations

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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 icon

Weekly Challenge 35: Clickety Click and All the Sixes

Stage: 5 Short Challenge Level: Challenge Level:1

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

problem icon

Succession in Randomia

Stage: 5 Challenge Level: Challenge Level:1

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

problem icon

OK! Now Prove It

Stage: 5 Challenge Level: Challenge Level:1

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

problem icon

Telescoping Series

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.

problem icon

Summats Clear

Stage: 5 Challenge Level: Challenge Level:1

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 icon

An Introduction to Mathematical Induction

Stage: 5

This article gives an introduction to mathematical induction, a powerful method of mathematical proof.

problem icon

Proof Sorter - Geometric Series

Stage: 5 Challenge Level: Challenge Level:1

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

problem icon

Clickety Click and All the Sixes

Stage: 5 Challenge Level: Challenge Level:1

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

problem icon

Picture Story

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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