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Marrrta [24]
3 years ago
5

Determine whether the sequence converges or diverges. If it converges, give the limit.

Mathematics
1 answer:
vaieri [72.5K]3 years ago
7 0

Answer:

The given series converges and \lim_{n \to \infty} a_n =0

Step-by-step explanation:

Given is 108, -18, 3,...

It is an alternate series. An alternate series is convergent if:

1. The series is decreasing.

2. If the last term (n-th term) of series converges to 0.

<u>Since each next term is less than its preceding term, so it is decreasing.</u>

First term, a = 108

Second term = -18

Common ratio, r = -18/108 = -1/6

General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ

<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>

Hence, the given series converges.

Now limit will be: \lim_{n \to \infty} a_n

\lim_{n \to \infty} 108*(-1/6)^n \\= 108*(-1/6)^\infty \\= 108*(1/\infty) \\= 108*0 \\= 0

Hence, \lim_{n \to \infty} a_n =0

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Mr. Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some brace
lisabon 2012 [21]

Answer: The equation is $29 + x*$4.50 = $42.50, and the solution is x = 3

Step-by-step explanation:

The data we have is:

Gonzales has $42.50

He wants to buy:

a shirt that costs $29

some bracelets that cost $4.50 each.

The equation that we need to solve is:

Total cost = money that Gonzales has.

The cost is $29 + x*$4.50

where x is the number of bracelets he can buy.

The equation that we need to solve is:

$29 + x*$4.50 = $42.50

to solve it we must isolate x:

x*$4.50 = $42.50 - $29 = $13.50

x = 13.50/4.50 = 3

So we have that Mr. Gonzales can buy a total of 3 bracelets.

8 0
3 years ago
Read 2 more answers
2.86 = ? tenths + 6 hundredths =
kherson [118]
To get 2.8 from 0.1 you have to multiply by 28. So 28 tenths. Which leaves 0.06 which is 0.01 times 6. So 6 hundredths
5 0
3 years ago
Read 2 more answers
A.45<br> B.30<br> C.90<br> D.180<br> E.40<br> F.55<br> G.130<br> H.50
cupoosta [38]

Answer:

If you were to make a 360 degree circle and minus the 50 thats already there you get 310 the right angle on angle 5 is 90 degrees because its a right angle so then the 310-90=220 the obtuse angle on angle 2 is 180 so 220-180=40 lastly you share those forty between angles 3 and 4 and the solution is your answer.

Glab to help!

7 0
3 years ago
Find the area of the shaded part in the given diagram
enyata [817]

Answer:

30cm^2

Step-by-step explanation:

area of large rectangle = length x width

= 5 X 9 = 45 cm^2

area of small rectangle = length x width

= 3 X 5 = 15 cm ^2

45 - 15 = 30cm^2

5 0
2 years ago
What is the slope of the linear function..........​
Sergio [31]

Answer:

-1

Step-by-step explanation:

slope: change in y divided by change in x

y2-y1/x2-x1

-11-(-5)/4-(-2)

-11+5/4+2

-6/6

-1

5 0
3 years ago
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