Mathematics Question Thread

[itssona]

why will this series have a limiting sum?
18+6+2+...

[RuiAce]

why will this series have a limiting sum?
18+6+2+...

The common ratio is 1/3, so its absolute value is 1/3 which is less than 1. Therefore it has a limiting sum.

[itssona]

The common ratio is 1/3, so its absolute value is 1/3 which is less than 1. Therefore it has a limiting sum.

ohh thank you!!
also i have this question- for what values of x does 1+(x-2)+(x-2)^2... converge and whats the limiting sum

so do i find r (which is x-2) and say that -1<x-2<1 so those are the values
and then to find limiting sum, i plug in those values? or am i off?

[RuiAce]

ohh thank you!!
also i have this question- for what values of x does 1+(x-2)+(x-2)^2... converge and whats the limiting sum

so do i find r (which is x-2) and say that -1<x-2<1 so those are the values
and then to find limiting sum, i plug in those values? or am i off?

You really should simplify \( -1 < x-2 < 1\) to \( 1 < x < 3\) first, but then just plug straight into the limiting sum formula. You'll get \( \frac{1}{1-(x-2)} \)

[itssona]

You really should simplify \( -1 < x-2 < 1\) to \( 1 < x < 3\) first, but then just plug straight into the limiting sum formula. You'll get \( \frac{1}{1-(x-2)} \)

oh so i leave it in the form 1/3-x ?

[jamonwindeyer]

oh so i leave it in the form 1/3-x ?

Yep!

[itssona]

Yep!

thank you

[gilliesb18]

Hey!
This is probably a regularly asked question, but How do I know how to write geometry proofs quickly and on the spot in an exam?
Anyone else struggle with this??

Thanks once again...

[jamonwindeyer]

Hey!
This is probably a regularly asked question, but How do I know how to write geometry proofs quickly and on the spot in an exam?
Anyone else struggle with this??

Thanks once again...

Hey! This is very much a practice makes perfect thing, you need to just do enough questions that it flows naturally! However, memorising the rules properly will help you write them succinctly, so make sure you do that. You are allowed to use symbols too. Don't be afraid to scribble out the proof using pro-numerals and labels on the exam sheet before actually writing out the proof, to give you a better idea of the path to the solution before you start

[gilliesb18]

Ok, thanks.
What I've been struggling with recently is writing out the proof, but then checking the answers and it has something completely different!! Probably a very very dumb question, but is there always more than one answer?
Thanks again

[RuiAce]

Ok, thanks.
What I've been struggling with recently is writing out the proof, but then checking the answers and it has something completely different!! Probably a very very dumb question, but is there always more than one answer?
Thanks again

Of course there is.

Why wouldn't there be? A question can be done in thousands of different ways and so long as the logic follows, each of those thousands of ways is a correct answer. The only time you can be wrong is if your logic and reasoning was incorrect

The "best" set of answers just demonstrates the "most optimal" method.

[gilliesb18]

Yep ok, that does make sense... dur me
Thanks!

[Mate2425]

Hi could i please get some help with this question (trapezoidal rule) thanks 😃
《 = integral, 1 = b , 0=a 

《^1 0  x^0.5 dx   using 5 subintervals

[RuiAce]

Hi could i please get some help with this question (trapezoidal rule) thanks 😃
《 = integral, 1 = b , 0=a 

《^1 0  x^0.5 dx   using 5 subintervals

[owidjaja]

Hey guys,

I need help with the following question:

Find any stationary points on the curve y=(4x^2-1)^4 and determine their nature.

Thanks!