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
shutvik [7]
3 years ago
7

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.
[infinity] n = 1 n2/5n n = 1
lim n→[infinity] an + 1/an =
a. converges
b. diverges
Mathematics
1 answer:
jeka57 [31]3 years ago
5 0

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

You might be interested in
Consider the circle with a 4 centimeter radius. If the length of major arc RT is 64 9 π, what is the measure of ∠RST?
grin007 [14]
25 degrees is the correct answer
8 0
3 years ago
Read 2 more answers
Solve for x<br> 20+.10x=50+.04x
maksim [4K]

Answer:

20 + .06x = 50

.06x = 30

x = 50

4 0
3 years ago
How many times dose 150 go into 1000
arsen [322]
\frac{\not1000^{20}} {\not150^{3}}=\frac{20}{3}= 6\frac{2}{3}\approx 6




3 0
3 years ago
Read 2 more answers
Helpppppppppppppppppppppppppppppppp
erik [133]
-8 * 2 =  -16

answer
C. -16
4 0
3 years ago
A set of exam scores is normally distributed and has a mean of 80.2 and a standard deviation of 11. What is the probability that
ZanzabumX [31]

Answer:

93.32% probability that a randomly selected score will be greater than 63.7.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 80.2, \sigma = 11

What is the probability that a randomly selected score will be greater than 63.7.

This is 1 subtracted by the pvalue of Z when X = 63.7. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{63.7 - 80.2}{11}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

1 - 0.0668 = 0.9332

93.32% probability that a randomly selected score will be greater than 63.7.

5 0
3 years ago
Other questions:
  • Can I have some help
    14·1 answer
  • Solve for a. 5a2=320
    9·2 answers
  • The area of a rectangle is 5x^3+19+6x-18 with length x + 3. Using synthetic division, what is the width of the rectangle?
    6·2 answers
  • Write the areas of the three triangles in terms of a, b, and<br> c.
    14·1 answer
  • What is the interquartile range of the following data set? 45,12,48,96,61,84,29,1,72,5,14
    6·2 answers
  • Show work for this scientific notation
    12·1 answer
  • For a line that goes through points (2,-2) and (1.-6), what is the equation
    8·1 answer
  • F(x)=log2(x-3) find the domain of x
    8·1 answer
  • B) Re-write the statement 16 + 5 + 2 - 1 by including one pair of brackets
    13·1 answer
  • Can someone PLEASE explain this im so confused?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!