Consider the following series. 1/6 + 1/12 + 1/18 + 1/24 + 1/30

Determine whether the series is convergent or divergent. Justify your answer.

a. Converges; the series is a constant multiple geometric series.
b. Converges; the limit of the terms, an, is 0 as n goes to infinity.
c. Diverges; the limit of the terms, an, is not 0 as n goes to infinity.
d. Diverges; the series is a constant multiple of the harmonic series.

If it is convergent, find the sum.

X+y=-4 x-y=2 use elimination with adding and subtraction

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

The numbers on a football field indicate 10 yard increments. you walk around the perimeter of a football field between the pylons. you walk a distance of 30623 yards. find the area and perimeter of the indicated regions. write your answers as mixed numbers, if necessary. a. one end zone: perimeter: yd area: yd2 b. the playing field (not including end zones): perimeter: yd area: yd2 c. the playing field (including end zones): perimeter: yd area: yd2