Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
1/(2^n)
(1+n)/(1+n^2)
1/4n^2+1
cos(n)*x/n^2
Integral of d{x}:
1/sqrt(1+x)
Derivative of:
1/sqrt(1+x)
Limit of the function:
1/sqrt(1+x)
Identical expressions
one /sqrt(one +x)
1 divide by square root of (1 plus x)
one divide by square root of (one plus x)
1/√(1+x)
1/sqrt1+x
1 divide by sqrt(1+x)
Similar expressions
1/sqrt(1-x)

Sum of series/ 1/sqrt(1+x)

Sum of series 1/sqrt(1+x)

The solution

You have entered [src]

  3            
____           
\   `          
 \        1    
  \   ---------
  /     _______
 /    \/ 1 + x 
/___,          
n = 1

\sum_{n=1}^{3} \frac{1}{\sqrt{x + 1}}

Sum(1/(sqrt(1 + x)), (n, 1, 3))

The answer [src]

    3    
---------
  _______
\/ 1 + x

\frac{3}{\sqrt{x + 1}}

3/sqrt(1 + x)

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
```