Summation of series

There are 31 NRICH Mathematical resources connected to Summation of series
Succession in Randomia
problem

Succession in randomia

Age
16 to 18
Challenge level
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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?
Summing squares
problem

Summing squares

Age
14 to 16
Challenge level
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Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Clickety Click
problem

Clickety click

Age
16 to 18
Challenge level
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What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
Degree Ceremony
problem

Degree ceremony

Age
16 to 18
Challenge level
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Can you find the sum of the squared sine values?
OK! Now prove it
problem

Ok! now prove it

Age
16 to 18
Challenge level
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Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
Proof Sorter - Geometric Sequence
interactivity

Proof sorter - geometric sequence

Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?
Sum the Series
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.
Powerful properties
article

Powerful properties

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