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Sum of series:
12(0.73)^(n-1)
1/(k*(k+1)*(k+2))
factorial(n+1)/n^n
1/((2n-1)(2n+3))
Identical expressions
twelve (zero . seventy-three)^(n- one)
12(0.73) to the power of (n minus 1)
twelve (zero . seventy minus three) to the power of (n minus one)
12(0.73)(n-1)
120.73n-1
120.73^n-1
Similar expressions
12(0.73)^(n+1)

Sum of series/ 12(0.73)^(n-1)

Sum of series 12(0.73)^(n-1)

The solution

You have entered [src]

  oo               
____               
\   `              
 \            n - 1
  \      / 73\     
  /   12*|---|     
 /       \100/     
/___,              
n = 1

\sum_{n=1}^{\infty} 12 \left(\frac{73}{100}\right)^{n - 1}

Sum(12*(73/100)^(n - 1), (n, 1, oo))

The radius of convergence of the power series

Given number:

12 \left(\frac{73}{100}\right)^{n - 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} = 12 \left(\frac{73}{100}\right)^{n - 1}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\left(\frac{73}{100}\right)^{- n} \left(\frac{73}{100}\right)^{n - 1}\right)

Let's take the limit
we find

False

False

False

The rate of convergence of the power series

The answer [src]

400/9

\frac{400}{9}

400/9

Numerical answer [src]

44.444444444444444444444444444

44.444444444444444444444444444

The graph

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Identical expressions

Similar expressions

Sum of series 12(0.73)^(n-1)

The solution

Examples of finding the sum of a series