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.

d. Diverges; the series is a constant multiple of the harmonic series.

Step-by-step explanation:

Given

Required

Determine if it diverges or converges

From the series, we have:

So, each term can be written as:

And the series is:

Recall that:

is known as the harmonic series, and it diverges to infinity

Hence: (d) is correct

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: