Expand ‘a’ in ascending powers up to and including the term x^3, stating the range of values of x for which the expansion is valid.

[orin]

In this problem (a) was easy, but I hit a wall on (b) I can’t seem to be able to find a solution. Anyone want to show me how it’s done? Expanding the thing is easy, but stating the range for which the expansion is valid?

 

[Deleted member 4993]

View attachment 17856
In this problem (a) was easy, but I hit a wall on (b) I can’t seem to be able to find a solution. Anyone want to show me how it’s done? Expanding the thing is easy, but stating the range for which the expansion is valid?

This will need you to look into the domain of validity of Taylor's series of expansion. Can you find those restrictions - and how those are applicable to this problem.

 

[HallsofIvy]

Or look at "Newton's generalized binomial theorem", http://mathonline.wikidot.com/newton-s-generalization-of-the-binomial-theorem
which extends the expansion of \(\displaystyle (x+ y)^n\) to the case where n is not an integer.