Why do this problem?
The problem gives practice in using the notation for Binomial
coefficients and manipulating algebraic expressions. In problem
solving mode, if they can't get started, they might first try to
work on the formula for small integer values of n.
Possible approach
Use as a revision exercise.
Key questions
If
æ ç
è
2n n
ö ÷
ø
is a binomial coefficient in the expansion of some
power of (1 + x) what can you say about the expansion and about the term
where it occurs?
What do we know about
æ ç
è
n r
ö ÷
ø
and
æ ç
è
n n-r
ö ÷
ø
?
Possible support
Ask learners to find the coefficient of x2 in the expansion of (1+x)4,
the coefficient of x3 in the expansion of (1 +x)6 and then the
coefficient of x4 in the expansion of (1 + x)8 and then ask them to try
to connect their results to the problem given.
You could ask students
to show that the sum of the nth row in Pascal's Triangle is 2n first - so
that they have a sense of achievement even if they don't succeed in proving the
result in this problem.