5 - 6 - 9 - 8 - 5 - 4 + 5 - 5 -5 -5 - 32 = ?
2 answers:
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EXPLANATION
The consecutive even numbers are
EXPLANATION
Let
be the first even number then, the next even number will be,
The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,
We multiply through with an LCM of 10 to get,
This simplifies to,
We expand the brackets to get,
We group like terms to get,
This simplifies to
Therefore the next even number is is
The consecutive even numbers are
EXPLANATION
Let
be the first even number then, the next even number will be,
The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,
We multiply through with an LCM of 10 to get,
This simplifies to,
We expand the brackets to get,
We group like terms to get,
This simplifies to
Therefore the next even number is is
Answer:
The Taylor series is .
The radius of convergence is .
Step-by-step explanation:
<em>The Taylor expansion.</em>
Recall that as we want the Taylor series centered at its expression is given in powers of
. With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of
.
Then,
Now, in order to make a more compact notation write . Thus, the above expression becomes
Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,
Now, substitute in the previous equality. Thus,
<em>Radius of convergence.</em>
We find the radius of convergence with the Cauchy-Hadamard formula:
Where stands for the coefficients of the Taylor series and
for the radius of convergence.
In this case the coefficients of the Taylor series are
and in consequence . Then,
Applying the properties of roots
Hence,
Recall that
So, as we get that
.