Mister Exam

### Other calculators

• #### How to use it?

• Sum of series:
• 1/4n^2-1
• 1/(n(lnn)((ln)(lnn))^2)
• factorial(n)/((n*n))
• (3-2i-5i^2+8i^3)
• #### Identical expressions

• one /4n^ two - one
• 1 divide by 4n squared minus 1
• one divide by 4n to the power of two minus one
• 1/4n2-1
• 1/4n²-1
• 1/4n to the power of 2-1
• 1 divide by 4n^2-1

• 1/4n^2+1

# Sum of series 1/4n^2-1

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### The solution

You have entered [src]
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\    / 2    \
\   |n     |
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n = 1         
$$\sum_{n=1}^{\infty} \left(\frac{n^{2}}{4} - 1\right)$$
Sum(n^2/4 - 1, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{n^{2}}{4} - 1$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = \frac{n^{2}}{4} - 1$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{\frac{n^{2}}{4} - 1}{\frac{\left(n + 1\right)^{2}}{4} - 1}}\right|$$
Let's take the limit
we find
True

False`
The rate of convergence of the power series