Mister Exam

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Sum of series:
7+k
(-1)^n/2n-1
(x-1)^n/3^n
sinn/sqrtn
Identical expressions
(- one)^n/2n- one
( minus 1) to the power of n divide by 2n minus 1
( minus one) to the power of n divide by 2n minus one
(-1)n/2n-1
-1n/2n-1
-1^n/2n-1
(-1)^n divide by 2n-1
Similar expressions
(1)^n/2n-1
(-1)^n/2n+1

Sum of series/ (-1)^n/2n-1

Sum of series (-1)^n/2n-1

The solution

You have entered [src]

  oo               
____               
\   `              
 \    /    n      \
  \   |(-1)       |
  /   |-----*n - 1|
 /    \  2        /
/___,              
n = 1

$$\sum_{n=1}^{\infty} \left(n \frac{\left(-1\right)^{n}}{2} - 1\right)$$

Sum(((-1)^n/2)*n - 1, (n, 1, oo))

The rate of convergence of the power series

The answer [src]

  oo                
____                
\   `               
 \    /           n\
  \   |     n*(-1) |
  /   |-1 + -------|
 /    \        2   /
/___,               
n = 1

$$\sum_{n=1}^{\infty} \left(\frac{\left(-1\right)^{n} n}{2} - 1\right)$$

Sum(-1 + n*(-1)^n/2, (n, 1, 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
```

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Identical expressions

Similar expressions

Sum of series (-1)^n/2n-1

The solution

Examples of finding the sum of a series