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1) In todays lesson we learned how to use and apply Gauss's Technique. In a sequence, for example 1 through 100 you may pair the terms form opposite ends, in this case 1+100 then find the sum of each pair which is 101 and finally multiply the number of pairs with the sum of each pair. There would be 50 pairs in total so you multiply 50 times the sum which is 101 and the final answer is 5050. By adding up all the numbers in the sequence from 1 to 100 the answer would be 5050. We aslo learned what is an arithmetic sequence: an indicated sum of the terms of an arithmetic sequence, and to find Sn for the fibonacci sequence.

2) An example is today's POD:
A business executive is offered one of tow raise schedules for the coming year:
option 1: receive a $100 raise each week
$100 $200 $300
option 2: receive a $1000 raise each month
$1000 $2000 $3000
which option should she choose?
how much more will she make with that option compared to the other option?
Solution:
weekly: 100+200+300--- 52 numbers
monthly: 1000+2000+3000---12 numbers
weekly: 100*26*53= $137,800
monthly: 1000*6*13=$78,000
weekly gives $59,800 more.
The reason why the step is to multiply 100x26x53 ies beacuase 100 is what is being added weekly, 26 is the half of the total weeks which are 52 and then multiply by the number of weeks but 1 has always to be added so is 53. The same for monthly, 1000 is being added, 6 is half of 12 months, and 12 months + 1 is 13.

3) Using Gauss's tecnique is very useful because for example lets say you have
1+2+3.....+n-2+n-1+n
adding opposite ends would always give n+1 so Sn which is the sum of the first n integers may be written as Sn= n(n+1)/2 this is an arithmetic series. Other way of writing the formula is n/2 (n+1). Another thing we learned was to find s5
for the fibonacci series. 1+1+2+3+5 so if all those numbers give the sum of 12. So s5 is 12.

The homework posted so far is to do exercises #'s 1 -8, pg.489.
For the next scribe post we choose Abraham and Mauricio to be the next pair to work on it for it.

Lala and Diego