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A Close Match
Can you massage the parameters of these curves to make them match as closely as possible?
Age 16 to 18 Short
Challenge Level
Find the sum of $$\frac{1}{\sqrt{1}+ \sqrt{2}}+ \frac{1}{\sqrt{2}+ \sqrt{3}} + \text{and so on up to}+\frac{1}{ \sqrt {99}+ \sqrt{100}}.$$
Can you invent any similar sums which have integer answers?
Did you know ... ?
Whilst this series can be summed using elementary methods mathematicians devise various ways in which the sums of series can be analysed. These are explored in greater detail in university analysis courses.
Whilst this series can be summed using elementary methods mathematicians devise various ways in which the sums of series can be analysed. These are explored in greater detail in university analysis courses.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.