Reccurence formula (1 Viewer)

[richz]

For those who have the 4u cambridge book. Ex 5.5 q 15 to 16. Dont flame me if i cant say this properly, its so hard to explain. How do u know what do u have to change the 2 parts. ie how do u know when to change the powers to n-1 or to n-2 etc?

thnx

 

[shafqat]

i sorta see wat ur saying, so here's a few tips

*you have to be able to do something when you split up lhs, so eg with q15 u need tanx^2, as u cant really do anything with tanx
but with sinx^n, n-1 is fine as u can integrate sinx
*also look at rhs for some hints. if there is an n-2 there, then u probably need to take lhs to n-2

hope this helps a litte :S

 

[richz]

that first pt u made is really helpful thnx
the 2nd pt u made is helpful in some ways, but isnt always the case.
My hypothesis is, by observing the: to show part, if the first part has a denominator of ie. in 15 n-1. i think u have to put a power of two, i think this would apply to others.

Have these questions been seen in past hsc papers? Because the hardest ones i have seen are partial fractions from the last 4 yrs

 

[shafqat]

yep, as i said for point 2, it is only probably true, but not always
and yes, your method is good too
as for hsc questions, im not sure, if it was it would be q 3-5 material
but i know that this sorta integration has been used in later qs like 7 and 8 for things such as the proof of the irrationality of e and i think pi as well