# Binomial Expansion : Finding Coefficients

Please see the attached file for the fully formatted problems.

Find the following:

a) The coefficient of x in the expansion of

b) The coeffiecient of in the expansion of

c) The coefficient of in the expansion of

d) The coefficient of in the expansion of is equal to the coefficient of in the expansion of. Find the value of a.

e) Write down the first four terms in the expansion of in ascending powers of x.

f) Without using a calculator, evaluate to 8 significant figures.

g) If , prove that

1)

2)

3)

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#### Solution Preview

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Find the following:

a) The coefficient of x in the expansion of

Solution. Since , the coefficient of x in the expansion of is ZERO.

b) The coeffiecient of in the expansion of

Solution. , so only can contain term . ...

#### Solution Summary

Coefficients are obtained from binomial expansions. Calculations are explained.