Submitted by Smhwang9 on Fri, 12/02/2016 - 13:31
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Can any one explain to me the solution for Assignment 3 warm up question (ii) please?
Submitted by Smhwang9 on Fri, 12/02/2016 - 13:31
Can any one explain to me the solution for Assignment 3 warm up question (ii) please?
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General overview
Could you specify the specific bit you don't understand? If you write $S_n = 1 + r + r^2 + \cdots +r^{n-1} + r^{n-1}$ then you can see that $rS_n = r + r^2 + \cdots + r^{n-1} + r^n$.
Can you simplify $rS_n - S_n = \bigg(r + r^2 + \cdots + r^{n-1} + r^n \bigg) - \ bigg(1 + r + r^2 + \cdots +r^{n-1} + r^{n-2} \bigg)$
Can you see which terms cancel? What do you get? Can you then see how if you have $rS_n - S_n = \text{something}$ then $S_n (r-1) = \text{something}$ so you can solve that equation for $S_n$? What happens if $r=1$? What fails?
Edited
Looks like you can't edit or delete posts on this forum? Weird. Anyway: fixed version:
Could you specify the specific bit you don't understand? If you write $S_n = 1 + r + r^2 + \cdots +r^{n-2} + r^{n-1}$ then you can see that $rS_n = r + r^2 + \cdots + r^{n-1} + r^n$
Can you simplify $$rS_n - S_n = \bigg(r + r^2 + \cdots + r^{n-1} + r^n \bigg) - \bigg(1 + r + r^2 + \cdots +r^{n-2} + r^{n-1} \bigg)$$
Can you see which terms cancel? What do you get? Can you then see how if you have $rS_n - S_n = \text{something}$ then $S_n (r-1) = \text{something}$ so you can solve that equation for $S_n$? What happens if $r=1$? What fails?