article
Sum the series
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.
Summation of series
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articlePowerful properties
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articleThe kth sum of n numbers
Yatir from Israel describes his method for summing a series of triangle numbers. -
articleAn introduction to mathematical induction
This article gives an introduction to mathematical induction, a powerful method of mathematical proof.
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articleSums of powers - a festive story
A story for students about adding powers of integers - with a festive twist. -
interactivityProof sorter - geometric sequence
Age16 to 18Challenge 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? -
problemSummats clear
Age16 to 18Challenge 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. -
problemSeriesly
Age16 to 18Challenge level
Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n! -
problemClickety click
Age16 to 18Challenge level
What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term? -
problemOK! Now prove it
Age16 to 18Challenge level
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?