Mister Exam

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• #### How to use it?

• Sum of series:
• cos(n)
• 16
• 7^(n+1)/(4^(n-2)*9^n)
• 10
• #### Identical expressions

• seven ^(n+ one)/(four ^(n- two)* nine ^n)
• 7 to the power of (n plus 1) divide by (4 to the power of (n minus 2) multiply by 9 to the power of n)
• seven to the power of (n plus one) divide by (four to the power of (n minus two) multiply by nine to the power of n)
• 7(n+1)/(4(n-2)*9n)
• 7n+1/4n-2*9n
• 7^(n+1)/(4^(n-2)9^n)
• 7(n+1)/(4(n-2)9n)
• 7n+1/4n-29n
• 7^n+1/4^n-29^n
• 7^(n+1) divide by (4^(n-2)*9^n)
• #### Similar expressions

• 7^(n-1)/(4^(n-2)*9^n)
• 7^(n+1)/(4^(n+2)*9^n)

# Sum of series 7^(n+1)/(4^(n-2)*9^n)

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### The solution

You have entered [src]
  oo
____
\
\       n + 1
\     7
)  ---------
/    n - 2  n
/    4     *9
/___,
n = 1          
$$\sum_{n=1}^{\infty} \frac{7^{n + 1}}{4^{n - 2} \cdot 9^{n}}$$
Sum(7^(n + 1)/((4^(n - 2)*9^n)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{7^{n + 1}}{4^{n - 2} \cdot 9^{n}}$$
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
$$a_{n} = 4^{2 - n} 7^{n + 1}$$
and
$$x_{0} = -9$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-9 + \lim_{n \to \infty}\left(4^{2 - n} 4^{n - 1} \cdot 7^{- n - 2} \cdot 7^{n + 1}\right)\right)$$
Let's take the limit
we find
False

False

$$R = 0$$
The rate of convergence of the power series
784
29
$$\frac{784}{29}$$
784/29
27.0344827586206896551724137931
27.0344827586206896551724137931`