Search by Topic

Resources tagged with Summation of series similar to Some Cubes:

Filter by: Content type:
Stage:
Challenge level:

Weekly Challenge 36: Seriesly

Stage: 5 Short Challenge Level:

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

Seriesly

Stage: 5 Challenge Level:

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

Telescoping Series

Stage: 5 Challenge Level:

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

An Introduction to Mathematical Induction

Stage: 5

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

Proof Sorter - Geometric Series

Stage: 5 Challenge Level:

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.

Weekly Challenge 34: Googol

Stage: 5 Short Challenge Level:

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

Speedy Summations

Stage: 5 Challenge Level:

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

Sums of Powers - A Festive Story

Stage: 3 and 4

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

Summing Geometric Progressions

Stage: 4 and 5 Challenge Level:

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

Slick Summing

Stage: 4 Challenge Level:

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

Summats Clear

Stage: 5 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.

Reciprocal Triangles

Stage: 5 Challenge Level:

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

Picture Story

Stage: 4 Challenge Level:

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

The Kth Sum of N Numbers

Stage: 5

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

More Polynomial Equations

Stage: 5 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.

OK! Now Prove It

Stage: 5 Challenge Level:

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

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.

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.

Overarch 2

Stage: 5 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?

Degree Ceremony

Stage: 5 Challenge Level:

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

Harmonically

Stage: 5 Challenge Level:

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

Production Equation

Stage: 5 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?

Succession in Randomia

Stage: 5 Challenge Level:

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?

Clickety Click and All the Sixes

Stage: 5 Challenge Level:

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

Weekly Challenge 35: Clickety Click and All the Sixes

Stage: 5 Short Challenge Level:

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