Answer:
The interval of convergence is:
Step-by-step explanation:
Given
The geometric series centered at c is of the form:
Where:
first term
common ratio
We have to write
In the following form:
So, we have:
Rewrite as:
Factorize
Open bracket
Rewrite as:
Collect like terms
Take LCM
So, we have:
By comparison with:
At c = 6, we have:
Take LCM
r = -\frac{1}{3}(x + \frac{11}{3}+6-6)
So, the power series becomes:
Substitute 1 for a
Substitute the expression for r
Expand
![\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B3x%20%2B%202%7D%20%3D%20%20%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%5B%28-%5Cfrac%7B1%7D%7B3%7D%29%5En%2A%20%28x%20-%20%5Cfrac%7B7%7D%7B3%7D%29%5En%5D)
Further expand:
The power series converges when:
Multiply both sides by 3
Expand the absolute inequality
Solve for x
Take LCM
The interval of convergence is:
There are 47,51,53,59,61,67,71, that is, 7 primes.
Answer:
y = 
x + 9
Step-by-step explanation:
Given parameters:
Coordinates = (-2,8)
Equation of the line y = 2x + 5;
Unknown:
Linear equation of a line perpendicular = ?
Solution:
From the given expression, a line perpendicular will have a negative inverse of the slope given.
y = 2x + 5
Equation of a line is y = mx + c;
y and x are the coordinates
m is the slope
c is the intercepts
y = 2x + 5 ;
The slope is 2;
A line perpendicular will have a slope of
Since y = 8 and x = -2, let us find c;
8 = 2 x + c
8 = -1 + c
c = 8+1 = 9
The equation of the line is;
y = x + 9
143/80 = 1 63/80 (use cymath!! it helps!!)
Answer:
First Area of the triangle=180 Degree
I,e ∠A+∠B+∠C=180°
Given ∠A= 21
∠B=34
∠C=X
∠A+∠B+∠C=180°
21+ 34+ x°=180°
55+x=180°
x°= 180-55
x= 125°
Step-by-step explanation:
