Math133 (1 Viewer)

[BenHowe]

Hey would anyone be able to help me with these 2 q's:

For this one I don't know how to do the series with 1/n




For this one I just dont understand the binomial form in general. Oops find the tayler series for it



Any help would be greatly appreciated!

 

[InteGrand]

Hey would anyone be able to help me with these 2 q's:

For this one I don't know how to do the series with 1/n

View attachment 34198


For this one I just dont understand the binomial form in general. Oops find the tayler series for it

View attachment 34199

Any help would be greatly appreciated!

 

[BenHowe]

Why is it -log(1-z)?

 

[InteGrand]

Why is it -log(1-z)?

It's one of the standard Taylor series. You can obtain it by integrating the geometric series.

 

[seanieg89]

You can also express the binomial coefficient in terms of factorials and powers of 2 if you like, but I leave that to you.

 

[seanieg89]

In case you haven't seen fractional binomial coefficients before:

 

[BenHowe]

It's one of the standard Taylor series. You can obtain it by integrating the geometric series.

So you can just the sum be J or whatever.



One question tho, do you get the right answer if multiply by x in the final step rather than shifting the sum so to speak i.e. integrand becomes 1/x(1-x)

 

[BenHowe]

In case you haven't seen fractional binomial coefficients before:

Yeah thanks heaps. I've done a lot of binomial stuff this semester in another unit, it just wasnt making sense. But just to clarify you can either do the general computation for tayler/macluaran series or you can fiddle with a function until it reduces a well-known result?

Thanks for your help