The Binomial Theorem for positive

The Binomial Theorem for positive, integral n

MathsDirect

What are the first 5 terms in the expansion of

We can use this expansion to make a quick approximation of (0.98)¹⁰.

If we say that
then

All the x terms are doing is moving the decimal points in the terms, so the sum is a very easy one

The calculator result is
so you can see that the expansion, only up to 5 terms, has given an answer, correct to 5 d.p.

Example 2

Find, to 3 d.p. the value of (1.03)⁷

We want to expand

So

The calculated value is