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alekssr [168]
3 years ago
13

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

nvergence or divergence of the series using other methods. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
[infinity]summation 7 n!/n = 1
Mathematics
1 answer:
Alex3 years ago
8 0

Answer:

Given series is divergent

Step-by-step explanation:

<u><em>Step(i):-</em></u>  

By using Ratio test

                \lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} }  | = l

a)     \lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} }  | = l  

'l' is finite then the given ∑aₙ is convergent

b)   \lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} }  | = l  

Here 'l' is infinite then the  ∑aₙ  is divergent

<u><em>Step(ii):-</em></u>

Given      aₙ = \frac{n!}{n}

            a_{n+1} = \frac{(n+1)!}{n+1}

     \lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} }  | = \lim_{n \to \infty} |\frac{\frac{(n+1)!}{n+1} }{\frac{n!}{n} } |

               we know that  n ! = n (n-1) (n-2) ......3.2.1

              and also          (n+1) ! = (n+1)n!

  \lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} }  | = \lim_{n \to \infty} |\frac{\frac{n+1)n!}{n+1} }{\frac{n!}{n} } |

\lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} }  | =  \lim_{n \to \infty} n

                       = ∞

<em>Given sum of the series is divergent</em>

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3 years ago
Priya is hosting a poetry club meeting this week and plans to have fruit punch and cheese for the meeting. She is preparing 8 ou
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Answer:

i) Number of people in club = 12

ii) 96 ounces of fruit punch for 12people

iii) 24 ounces of cheese for 12 people

iv) Priya's budget for poetry club meeting in dollars = $7.87

Step-by-step explanation:

We are not given the options for the equations that could represent the quantities and constraints in this situation. We can tell we are to represent the information given above.

Number of people in the club = 12

8 ounces of fruit punch per person

For 12 people = 12×8 = 96 ounces of fruit punch

2 ounces of cheese per person

For 12 people = 12×2 = 24 ounces of cheese

A package of cheese = 16 ounces

The costs for 1package = $3.99

The costs for 16 ounces of cheese = $3.99

The cost for 24 ounces of cheese = (24×3.99)/16 = 5.985

The cost for 24 ounces of cheese = $5.99

One-gallon jug of fruit punch = 128 ounces

The cost of One-gallon jug of fruit punch = $2.50

The costs of 128 ounces of fruit punch = $2.50

The costs for 96 ounces of fruit punch = (96×2.5)/128 = 1.875

The costs for 96 ounces of fruit punch = $1.88

Priya's budget for poetry club meeting in dollars = $5.99 + $1.88 = $7.87

Cost per item for x number of people:

y = x(2.5/128) + x (3.99/16)

y = x(0.0195) + x(0.2494)

Cost equation for Priya's budget:

y = 96x(2.5/128) + 24x (3.99/16)

y = 96x(0.0195) + 24x(0.2494)

Since the total number of people to attend the meeting is 12, the constraint = 0≤x≤12

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B. Y=2x

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You put $500 in the bank, where it ears 1.5% simple interest every year. How long until your money will triple?
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Answer:

133.33 years

Step-by-step explanation:

Given that:

Principal = $500

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