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Math Challenge IC Handout Assignment 4

 
 
Picture of Christina Peng
Math Challenge IC Handout Assignment 4
by Christina Peng - Tuesday, 20 March 2018, 11:11 PM
 

For 4.16, I feel like none of those equations work when I plug in the numbers. They all turn positive or all turn negative. Is there something I'm missing? Also, I am having trouble thinking of how to find a formula for the sum generally for a geometric sequence on 4.29 (a and (b.  Would it be okay if you gave me a few tips?


Thanks a bunch!

 
Picture of David Reynoso
Re: Math Challenge IC Handout Assignment 4
by David Reynoso - Tuesday, 27 March 2018, 1:13 PM
 

Question 4.16 had a mistake that has now been corrected.

For 4.29 a useful trick is to multiply the whole series by $r$, that is, if you have the sum with $n$ terms $S_n = \displaystyle \sum_{k=0} ^{n-1} a_0\cdot r^k = a+ar+ar^2+\cdots+ar^{n-1} $, $r$ times that sum is equal to $r\cdot S_n = ar + ar^2 + ar^3 + \cdots + ar^n$. Note that these two ($S_n$ and $r\cdot S_n$) have a lot of terms in common. You can use this two expressions to solve for the sum $S_n$.

Picture of Christina Peng
Re: Math Challenge IC Handout Assignment 4
by Christina Peng - Wednesday, 4 April 2018, 1:11 AM
 

Thank you!