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Sum of series:
200(0.98)^n-1
(3x^2-2x+3)(x+1)^x
sqrt(n)*(n/(4*n-3))^(2*n)
arcctg((n+1)/(n^2-3))
Identical expressions
two hundred (zero . ninety-eight)^n- one
200(0.98) to the power of n minus 1
two hundred (zero . ninety minus eight) to the power of n minus one
200(0.98)n-1
2000.98n-1
2000.98^n-1
Similar expressions
200(0.98)^n+1

Sum of series/ 200(0.98)^n-1

Sum of series 200(0.98)^n-1

The solution

You have entered [src]

  oo                 
____                 
\   `                
 \    /        n    \
  \   |    /49\     |
  /   |200*|--|  - 1|
 /    \    \50/     /
/___,                
n = 1

\sum_{n=1}^{\infty} \left(200 \left(\frac{49}{50}\right)^{n} - 1\right)

Sum(200*(49/50)^n - 1, (n, 1, oo))

The radius of convergence of the power series

Given number:

200 \left(\frac{49}{50}\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} = 200 \left(\frac{49}{50}\right)^{n} - 1

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} \left|{\frac{200 \left(\frac{49}{50}\right)^{n} - 1}{200 \left(\frac{49}{50}\right)^{n + 1} - 1}}\right|

Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

-oo

-\infty

-oo

Numerical answer

The series diverges

The graph

Examples of finding the sum of a series

The Sum of the Power Series
```
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```
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```
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```
1/2^(n!)
```
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```
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```
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```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
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1/n^4
```
```
1/n^6
```
Harmonic series
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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 200(0.98)^n-1

The solution

Examples of finding the sum of a series