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:
Step-by-step explanation:
Find attached the first sum.
x denotes horizontal and y denotes vertical
When the value of x is positive, it moves to right side and when x is negative, it moves left sides 'x unit'
When the value of y is positive, it moves to up side and when y is negative, it moves down sides 'y unit'
Answer: micheal Jackson!
Step-by-step explanation:
Answer:
see the attachment
Step-by-step explanation:
The graph attached shows the secant function in red. The restriction to the interval [0, π/2] is highlighted by green dots, and the corresponding inverse function is shown by a green curve.
The restriction to the interval [π/2, π] is highlighted by purple dots, and the corresponding inverse function is shown in purple.
The dashed orange line at y=x is the line over which a function and its inverse are mirror images of each other.
Evaluate f(8) for the given function.
f(8) = 7(8)-3 = 53
answer: 53