Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
n*2^n
sinn/n
1/(x*(x+1))
-18
Identical expressions
(pi/ two (n))sen(pi(i)/ two (n))
( Pi divide by 2(n))sen( Pi (i) divide by 2(n))
( Pi divide by two (n))sen( Pi (i) divide by two (n))
pi/2nsenpii/2n
(pi divide by 2(n))sen(pi(i) divide by 2(n))
Similar expressions
pi/((2*n))sen(pi(i)/2(n))

Sum of series (pi/2(n))sen(pi(i)/2(n))

The solution

You have entered [src]

  oo                  
 ___                  
 \  `                 
  \   pi      /pi*i  \
   )  --*n*sin|----*n|
  /   2       \ 2    /
 /__,                 
i = 1

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

Sum(((pi/2)*n)*sin(((pi*i)/2)*n), (i, 1, oo))

The answer [src]

  oo                  
____                  
\   `                 
 \            /pi*i*n\
  \   pi*n*sin|------|
   )          \  2   /
  /   ----------------
 /           2        
/___,                 
i = 1

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

Sum(pi*n*sin(pi*i*n/2)/2, (i, 1, oo))

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 (pi/2(n))sen(pi(i)/2(n))

The solution

Examples of finding the sum of a series