Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
1/n(n+1)
sqrt(n+1)/2^n
x^(2n)/(2n)!
1/((3*n-1)*(3*n+2))
Identical expressions
one /n(n+ one)
1 divide by n(n plus 1)
one divide by n(n plus one)
1/nn+1
1 divide by n(n+1)
Similar expressions
1/(n(n+1)(n+2))
1/(n*(n+1)*(n+2))
1/n(n-1)
1/n*(n+1)
(n-1)/(n(n+1)(n+2))
x^(n+1)/(n(n+1))

Sum of series/ 1/n(n+1)

Sum of series 1/n(n+1)

The solution

You have entered [src]

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

\sum_{n=1}^{\infty} \frac{n + 1}{n}

Sum((n + 1)/n, (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{n + 1}{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} = \frac{n + 1}{n}

and

x_{0} = 0

,

d = 0

,

c = 1

then

1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right)^{2}}{n \left(n + 2\right)}\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

Sum of series 1/n(n+1)

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
```