sky724
11.06.2020 •
Mathematics
Consider the following geometric series.
[infinity]∑n=1 (−8)n−19n
a) Find the common ratio.
b) Determine whether the geometric series is convergent or divergent.
c) If it is convergent, find its sum. (If the quantity diverges, answer diverges.)
Solved
Show answers
More tips
- F Food and Cooking What s the Best Rice for Cooking Plov?...
- F Family and Home How to Remove Fading from Clothes: Tips and Tricks...
- F Food and Cooking How to Make Polendwitsa at Home?...
- F Family and Home Parents or Environment: Who Has the Most Influence on a Child s Upbringing?...
- P Philosophy Unbelievable stories of encounters with otherworldly forces...
- L Leisure and Entertainment How to Choose the Perfect Gift for Men on February 23rd?...
- H Health and Medicine How to Treat Whooping Cough in Children?...
- H Health and Medicine Simple Ways to Lower Cholesterol in the Blood: Tips and Tricks...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
Answers on questions: Mathematics
- M Mathematics Find the radius of the sphere with a volume of cubic yards. Write your answer as a fraction in simplest form. Please show work too. Thank you. :)...
- M Mathematics What do you think? What is the answer for this ?...
- M Mathematics For which pair of functions is (g*f)(a) = /a/-2?...
- M Mathematics Use the formula about to calculate the area of that circle....
- M Mathematics For the sequence -28,-16,-4,8,... The expression that defines the nth term where a 1 =-28 is 12 - 28n 2 12 - 28(n - 1) 3. - 28 + 12n - 28 + 12(n - 1) Submit Answer...
- M Mathematics Oliver is playing a game in which he has to choose one of three numbers (3,4, or 9) and then one of five vowels (a,e,i,o,u) how many possible outcomes are there?...
- M Mathematics Please help im very confused...
- M Mathematics PLEASE HELP! Which of the following is a polynomial?...
- M Mathematics 5 Find the quotient. (2x4 - 3x3 - 6x2 + 11x + 8) = (x - 2) Circle the best choice: 2x3 – 7x² + 8x - 5 + 1 - 2 2x² + x² - 4x + 3 + 4 4x² + 2x² – 8x + 6 + 1 4x² – 14x² + 16x...
- M Mathematics Which could be the equation for the function shown in the graph?...
Ответ:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
Ответ:
3√128
Step-by-step explanation: