Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
7x²
(2n+6)*tg(15/(9n+11))
3*n/log(3*n)
1/i
Identical expressions
(i+ one)/(i)
(i plus 1) divide by (i)
(i plus one) divide by (i)
i+1/i
(i+1) divide by (i)
Similar expressions
-1^(i+1)/i!
(i+1)/i
(i-1)/(i)

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

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

The solution

You have entered [src]

  oo       
 ___       
 \  `      
  \   i + 1
   )  -----
  /     i  
 /__,      
i = 2

$$\sum_{i=2}^{\infty} \frac{i + 1}{i}$$

Sum((i + 1)/i, (i, 2, oo))

The radius of convergence of the power series

Given number:
$$\frac{i + 1}{i}$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = \frac{i + 1}{i}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{\left(i + 1\right)^{2}}{i \left(i + 2\right)}\right)$$
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

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
```

Other calculators

How to use it?

Identical expressions

Similar expressions

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

The solution

Examples of finding the sum of a series