Mister Exam

Lang:

Other calculators

n^2/e^(sqrt(n))

How to use it?
Sum of series:
n^2*x^(n-1)
(2*n-3)/(n^2+2)
n^2/e^(sqrt(n))
ln((n^3-1)/(n^3+1))
Identical expressions
n^ two /e^(sqrt(n))
n squared divide by e to the power of ( square root of (n))
n to the power of two divide by e to the power of ( square root of (n))
n^2/e^(√(n))
n2/e(sqrt(n))
n2/esqrtn
n²/e^(sqrt(n))
n to the power of 2/e to the power of (sqrt(n))
n^2/e^sqrtn
n^2 divide by e^(sqrt(n))

Sum of series/ n^2/e^(sqrt(n))

Sum of series n^2/e^(sqrt(n))

The solution

You have entered [src]

  oo         
_____        
\    `       
 \        2  
  \      n   
   \   ------
   /      ___
  /     \/ n 
 /     E     
/____,       
n = 1

$$\sum_{n=1}^{\infty} \frac{n^{2}}{e^{\sqrt{n}}}$$

Sum(n^2/E^(sqrt(n)), (n, 1, oo))

The rate of convergence of the power series

The answer [src]

  oo            
 ___            
 \  `           
  \          ___
   )   2  -\/ n 
  /   n *e      
 /__,           
n = 1

$$\sum_{n=1}^{\infty} n^{2} e^{- \sqrt{n}}$$

Sum(n^2*exp(-sqrt(n)), (n, 1, oo))

Numerical answer [src]

239.994930345328242743435897448

239.994930345328242743435897448

The graph

Sum of series n^2/e^(sqrt(n))

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
```