I have a question could you please elaborate the step with the ln summation. I didn't get that part where the ln addition of all terms led us to o and 6720. Thank You very much
That part was calculated manually since the bounds were small enough. Just the sum for those 6 terms and brought them back in to the logarithm using the product rule. The rightmost sum can technically be done faster using another type of factorial, but I hadn't covered that here. Usually the conversion to a sum isn't always the most helpful, except for checking for convergence since there aren't many summation formulas with ln(x). But I wanted to show some context where it could technically be applied.
I just put that there for aesthetic and to showcase the construct haha. It isn't that hard to calculate if you are up to it, just that the result is very small. You need to split the product by division, reset index, and eventually arrive at 6627 / 2(47!).
@@MichaelMaths_ i thik my answer is also correct you just need to multiply and divide 47 to the answer which I got in order to get that answer which u have written, well thanks for replying
I was looking for the rules of pi product rules.and i got here finally.thanks man❤❤❤
I have a question could you please elaborate the step with the ln summation. I didn't get that part where the ln addition of all terms led us to o and 6720. Thank You very much
That part was calculated manually since the bounds were small enough. Just the sum for those 6 terms and brought them back in to the logarithm using the product rule. The rightmost sum can technically be done faster using another type of factorial, but I hadn't covered that here. Usually the conversion to a sum isn't always the most helpful, except for checking for convergence since there aren't many summation formulas with ln(x). But I wanted to show some context where it could technically be applied.
@@MichaelMaths_ thanks 👌
nice explanation!
Great video
the second worked example, im confused as to where x-5 came from? could you please explain
That was just from normal trinomial factoring and then splitting the product for each factor
Is the product notation the same as the sigma notation?
They both combine many indexed items, but product notation multiplies everything together while sigma notation adds everything together.
Thnx very helpful
That reset index formula works for anything inside the capital pi though right? Not just k?
Oh yeah, it does. I think in the moment I forgot to just show it as any expression, good catch 👍
6:22 how do you get 2
The upper bound of the denominator is the original lower bound minus 1. The original is 3, so you get 3-1=2
Where is the thumbnail question
I just put that there for aesthetic and to showcase the construct haha. It isn't that hard to calculate if you are up to it, just that the result is very small. You need to split the product by division, reset index, and eventually arrive at 6627 / 2(47!).
@@MichaelMaths_ i thik my answer is also correct you just need to multiply and divide 47 to the answer which I got in order to get that answer which u have written, well thanks for replying
❤❤❤❤ thanks a lot
Thnx bro