[4 - (3c - 1)][6 - ( 3c - 1)]
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The power series is
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence
The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.
Its radius of convergence is 0.5
Let,
f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....
The power series expansion (geometric series),
valid for I2xI < 1 , IxI < 0.5
so, radius of convergence = 0.5
The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5
Now, g(x) = ln(1-2x)
= -2
=-2
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
is the power series expansion for g(x).
radius of convergence =0.5
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The median is the value that can be found in the middle of any data set. After plotting the values on the line plot (shown in the attached image), we can write out our data (shown under neath the line plot).
Then, we start by crossing off one value on each side of the data to work our way towards the middle. Once we come to the middle, we see that there are two values in the middle: 6 and 6.
To find the median when we have two values in the middle, we must add them, then divide by two.
6 + 6 = 12
12 ÷ 2 = 6
So, the median for this data set is 6.
Then, we start by crossing off one value on each side of the data to work our way towards the middle. Once we come to the middle, we see that there are two values in the middle: 6 and 6.
To find the median when we have two values in the middle, we must add them, then divide by two.
6 + 6 = 12
12 ÷ 2 = 6
So, the median for this data set is 6.