Not sure what this notation is asking me?

luciahz

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Hi, sorry if this is the wrong category but I'm not too sure what the notation in this question means. I maybe understand a) but don't get the rest.
 

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blamocur

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I maybe understand a) but don't get the rest.

By "the rest" you mean (b)? If that's the case what makes (b) more confusing than (a)?
 

Dr.Peterson

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Hi, sorry if this is the wrong category but I'm not too sure what the notation in this question means. I maybe understand a) but don't get the rest.
If you at least understand what (a) means, then the notation is probably not the issue.

Have you considered expanding the summand in (b), and using the results of (a)?

But first, it sounds like you haven't actually solved any of (a). I'm guessing that you've learned the binomial theorem; what else have you learned that might be useful? The more you tell us, specifically, about what you do and don't know, the better we can help.
 

luciahz

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If you at least understand what (a) means, then the notation is probably not the issue.

Have you considered expanding the summand in (b), and using the results of (a)?

But first, it sounds like you haven't actually solved any of (a). I'm guessing that you've learned the binomial theorem; what else have you learned that might be useful? The more you tell us, specifically, about what you do and don't know, the better we can help.
I know binomial theorem and basic sigma notation (like Σ n(n+1) kind of thing), but I'm not sure what the a_k x^k means and how to apply that to (2-x)^n. is a_k a constant?

What I mean by I sort of understand a) is that I understood it as sub in x=1 and prove with induction, which is probably incorrect
 

luciahz

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Sorry, I just realised that I misread. I meant that I maybe understood part ai, and was asking for help on aii, not part b.
If you at least understand what (a) means, then the notation is probably not the issue.
 

Dr.Peterson

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I know binomial theorem and basic sigma notation (like Σ n(n+1) kind of thing), but I'm not sure what the a_k x^k means and how to apply that to (2-x)^n. is a_k a constant?

What I mean by I sort of understand a) is that I understood it as sub in x=1 and prove with induction, which is probably incorrect
Sorry, I just realised that I misread. I meant that I maybe understood part ai, and was asking for help on aii, not part b.
The [imath]a_k[/imath] are the coefficients in the expansion. Yes, they are constants. It may help if you work out the details for a specific value of n, such as 3 or 4. What is the expansion of [imath]2-x)^3[/imath]? What are the coefficients? What do the three parts of (a) mean in that specific case?

Your approach to (a i) is good; but you may be going wrong in assuming you can do exactly the same for the others. You may need to use results from the binomial theorem, together with induction. (I haven't tried it yet.)
 

blamocur

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After following @Dr.Peterson advice can you complete and post the solution for a.i) ?
Also, are familiar with derivatives?
 

Dr.Peterson

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After following @Dr.Peterson advice can you complete and post the solution for a.i) ?
Also, are you familiar with derivatives?
This reminds me that I intended to add that induction is not necessarily required for (a i); I affirmed that mostly on the assumption that induction may be what the OP is expected (or at least expects) to use.

Since we don't know the context, it is quite possible that other methods (including derivatives, despite the subject being algebra) might also be available.
 
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