1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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>

You might be interested in
Kira needs 3,000 milligrams of zinc for a science experiment. Which expression can be used to determine how many grams of zinc s
harina [27]

Answer: 3,000 divided by a thousand

Step-by-step explanation: 1,000 milligrams equal one gram so you divide the number of milligrams by 1,000 to find out the number of grams.

8 0
3 years ago
Candy bars are sold in a local store for 90 cents each. The factory has $1500 in fixed costs plus 10 cents of additional expense
pychu [463]

Answer:

Produce of 2000 candy bars is the break even point.

Step-by-step explanation:

4 0
3 years ago
If x= -3, and -3 = y, then what can be said about the relationship between x and y? Explain
ella [17]

I'd say that the relationship between y and x is that they're both equivalent to each other, since -3 = -3.

7 0
3 years ago
Read 2 more answers
Is x^2-1 a polynomial
77julia77 [94]

Answer:

Yes it's a binomial.

Step-by-step explanation:

A polynomial is an expression with more than one term that often has variables and exponents on the variable. Since this has two terms separated by a subtraction sign with one term being a variable to the exponent of 2 then this is a polynomial. It is called a binomial. More than 2 terms are referred exclusively as a polynomial with ___ terms.

4 0
3 years ago
Find the factored form of<br> 11m + m2 = 0
Vlada [557]

Answer:

Step-by-step explanation:

If you want to factor

m^2+11m=0,  you could throw that into the quadratic formula with a = 1, b = 11 and c = 0, but the easier thing to do is to factor out what's common in those 2 terms.  m is common, so when we factor it out:

m(m+11)=0

That's the factored form.

By the Zero Product Property, either

m = 0 or m + 11 = 0.  

So the 2 solutions to this are

m = 0 or m = -11

Not sure how far you need to go with this.

3 0
2 years ago
Read 2 more answers
Other questions:
  • Name the property the equation illustrates. -2.1x1=-2.1
    12·1 answer
  • Find the unit rate with the second given unit in the denominator.
    5·1 answer
  • Michael Rice’s bike at a constant speed of 12 mph how far can he travel in two hours
    14·2 answers
  • Thirty is 12% of what number?
    7·1 answer
  • Give three numbers between 8 and -8
    15·2 answers
  • The lab experiment is repeated again with the same two glass plates and the same sodium lamp but with a different human hair. Th
    12·1 answer
  • What is the product of (2p + 7)(3p2 + 4p – 3)?
    8·2 answers
  • I really need help for this! Please!
    10·1 answer
  • !Can some1 help! !Help FAST!
    10·2 answers
  • ACTIVITY 2 Continued
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!