(6 points) Select the FIRST correct reason why the given series converges. A. Convergent geometric series B. Convergent p series C. Comparison (or Limit Comparison) with a geometric or p series D. Alternating Series Test E. None of the above

C. Comparison ( or limit of of comparison) with a geometric or p series.

Step-by-step explanation:

Let say we consider the series

S

=

∞

∑

n

=

1

a

n

.

For brevity, lets that assume

a

n

≥

0.

A common technique or way use for determining the convergence or divergence of a series is the the comparison test is. In a summarize detail, if we are able to show that the terms of S are bounded below by the terms of divergent series then we know that S diverges as well. Also, if can be able to bound the terms of S above by the terms of a convergent series then S will also converges as well. We commonly compare series to the geometric or p-series. A geometric series is of the form

∞

∑

n

=

0

r

n

and is convergent if

|

r

|

<

1.

A p-series is of the form

∞

∑

n

=

0

1

n

p

and it is convergent if

p

>

1.

14

step-by-step explanation:

14 x 3 = 42

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3