Binomial Series (Edexcel IGCSE Further Pure Maths): Exam Questions

Show that

where and are positive integers.

The expansion of in ascending powers of can be written as

where , , and are rational numbers.

Show that and

and find and in terms of and , as fractions in their lowest terms.

Given that and

show that = 3 and =1

Hence, using an appropriate value of , find, to 3 decimal places, an approximate value for

Expand in ascending powers of up to and including the term in

Where appropriate express each coefficient as an exact fraction in its lowest terms.

Write down the range of values of for which your expression is valid.

Express in the form where and are rational numbers whose values should be stated.

Obtain a series expansion for in ascending powers of up to and including the term in

Expand in ascending powers of , up to and including the term in giving each coefficient as an integer.

where and are prime numbers

Given that the fourth and fifth terms, in ascending powers of , in the series expansion of are 20and 48 respectively,

find the value of and the value of

Given that can be expressed in the form where and are constants,

find the value of and the value of

Hence, expand in ascending powers of up to and including the term in ² , expressing each coefficient as an exact fraction in its lowest terms.

Using the expansion found in part (b) with a suitable value of

show that