Answer:
The series is convergent answer ⇒ (a)
Step-by-step explanation:
* The series is -8/5 + 32/25 + -128/125 + ........
- It is a geometric series with:
- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -4/5
∴ IrI = 4/5
∴ IrI < 1
∴ The series is convergent
Answer:
y variable will be elimited when adding the system of equations
x = 2 or y = 3
Step-by-step explanation:
- x + 6y = 16
8x - 6y = -2
Add both equations
(-x + 8x) + {6y + (-6y)} = 16 + (-2)
7x + 6y - 6y = 16 - 2
7x + 0 = 14
7x = 14
x = 14/7
x = 2
- x + 6y = 16
- 2 + 6y = 16
6y = 16 + 2
6y = 18
y = 18/6
y = 3
the x variable will be eliminating when adding the system of equations and the
y variable will be elimited when adding the system of equations
or the sum of the system equations is negative 8X = 14 or
x = 2 or y = 3
or there's only one solution to the system equations
Answer:
k = -8
Step-by-step explanation:
−3 + 3k = −27
⇔ -3 + 3k +3 = -27 +3
⇔ 3k = -24
⇔ k = -8
Jeremy will pay $41.05 interest.
We know that, Interest = PRT/100
where,
P = principal
R = rate
T = time
For given question, principal (P) = $325.18
interest rate R = 12 5/8%
= 12.625%
And period T = 1 year
We need to find the interest.
⇒ Interest = PRT/100
⇒ Interest = (325.18 × 12.625 × 1) / 100
⇒ Interest = 4105.3975 / 100
⇒ Interest = $41.05
Therefore, Jeremy will pay $41.05 interest.
Learn more about the interest here:
brainly.com/question/15052754
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