Mister Exam

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Sum of series:
(w+1)/w
sinx
(1+(-3)^n)/6^n
(3^n+2^n)/6^n
Identical expressions
(w+ one)/w
(w plus 1) divide by w
(w plus one) divide by w
w+1/w
(w+1) divide by w
Similar expressions
(w-1)/w

Sum of series/ (w+1)/w

Sum of series (w+1)/w

The solution

You have entered [src]

  oo       
 ___       
 \  `      
  \   w + 1
   )  -----
  /     w  
 /__,      
y = 1

\sum_{y=1}^{\infty} \frac{w + 1}{w}

Sum((w + 1)/w, (y, 1, oo))

The radius of convergence of the power series

Given number:

\frac{w + 1}{w}

It is a series of species

a_{y} \left(c y - y_{0}\right)^{d y}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{y_{0} + \lim_{y \to \infty} \left|{\frac{a_{y}}{a_{y + 1}}}\right|}{c}

In this case

a_{y} = \frac{w + 1}{w}

and

y_{0} = 0

,

d = 0

,

c = 1

then

1 = \lim_{y \to \infty} 1

Let's take the limit
we find

True

False

The answer [src]

oo*(1 + w)
----------
    w

\frac{\infty \left(w + 1\right)}{w}

oo*(1 + w)/w

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
```