Part 1.] in two or more complete sentences, describe the difference between an infinite series and a finite series.

part 2.] in two or more complete sentences, explain why the following sequence is an example of a finite series.
2 + 4 + 8 + 16 + 256

part 3.] in two or more complete sentences describe why the following series is an example of an infinite series.
1 + 2 + 3 + 4 + 5 +

part 4.] the first picture

part 5.] express the series in summation notation.
2 + 4 + 6 + 8 + 10 + 12

part 6.] suppose you start an annuity where you invest $2,000 at the beginning of each year and 4% interest is paid at the end of the year. what is the value of the annuity at the end of 5 years, rounded to the nearest dollar? it is $

part 7.] find the sum picture

1) A series is called finite, if there is a finite number of factors that need to be added. If there are infinitely many factors (after any finite number of additions, there are still factors to add), then it is called infinite.
2) We have that this is the sup of powers of 2; but it does not take all powers of 2, only until the 8th power of 2. Hence, there are 8 summants, a finite number.
3) We have that this series involves all the natural numbers; "..." means that we should continue adding the next term, meaning that there is no end.
4) In order to find the first term of the series, we need to substitute n=1. Hence the first term is 1/(2*1+1)=1/3. Similarly, the next term is equal to 2/(2*2+1)=2/5
5) We notice that the first term is 2 and then that all the terms are 2 higher than their previous one. Hence we have that if we start summation from 1, we need to double it to get the term. This works for all and hence we have that the series is equal to: .
6) We have that after one, year, he gains 4%*2000, hence the final amount is 1.04*2000 after one year. Next year, this becomes the capital and we have to multiply again by 1.04. Hence, after 5 years, the total annuity value is: (1.04)^5*2000=2433$.
7) We have that the sum is 4+7+... up until 3*12+1=37. The sum of those is 246 or else we can have that it is equal to 3* n(n+1)/2+12 where n=12 (The sum of all numbers from 1 to n is given by n*(n+1)/2 )

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