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## 'Growing' printed from http://nrich.maths.org/

Why do this problem?

The numerical examples should prompt learners to formulate and
prove a more general statement and then apply it to these special
cases. Going from the particular to the general in problem solving
is an important skill for a mathematician.

Inequalities play a big role in advanced mathematics and
mathematical research and learners in school will benefit from
experience of working with inequalities.

They need to know the Binomial Theorem and the formula for the
exponential series and then the problem gives experience of
applying these formulae and of proof by mathematical
induction.

Possible approach

The first part could be a lesson starter or homework in preparation
for a lesson or you could do the first part as a class and set the
two numerical examples to be done independently.

Key questions

How do the numerical examples relate to $(1 +\frac{1}{n})^n$?