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Mathematical modelling. Tree diagrams. Combining probabilities. Probability. Biology. Theoretical probability. Conditional probability. Equally likely outcomes. Experimental probability. Spreadsheets.There are 30 results
Broad Topics > Patterns, Sequences and Structure > Summation of series
Succession in Randomia
Age 16 to 18
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?
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?
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?
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 ?
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.
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?
Sums of Powers - A Festive Story
Age 14 to 18
A story for students about adding powers of integers - with a festive twist.
Summing Geometric Progressions
Age 14 to 18
Challenge Level
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Slick Summing
Age 14 to 16
Challenge Level
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Speedy Summations
Age 16 to 18
Challenge Level
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
Googol
Age 16 to 18 Short
Challenge Level
Find the smallest value for which a particular sequence is greater than a googol.
Seriesly
Age 16 to 18 Short
Challenge Level
Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!
Clickety Click
Age 16 to 18 Short
Challenge Level
What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
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?
An Introduction to Mathematical Induction
Age 16 to 18
This article gives an introduction to mathematical induction, a powerful method of mathematical proof.
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!
Degree Ceremony
Age 16 to 18
Challenge Level
What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
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.
OK! Now Prove It
Age 16 to 18
Challenge Level
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
Telescoping Series
Age 16 to 18
Challenge Level
Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
2^n -n Numbers
Age 16 to 18
Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.
Sum the Series
Age 16 to 18
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.
Clickety Click and All the Sixes
Age 16 to 18
Challenge Level
What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
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?
The Kth Sum of N Numbers
Age 16 to 18
Yatir from Israel describes his method for summing a series of triangle numbers.
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.
A Swiss Sum
Age 16 to 18
Challenge Level
Can you use the given image to say something about the sum of an infinite series?
NRICH is part of the family of activities in the Millennium Mathematics Project.