Mister Exam

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Sum of series:
1/(n(n+1))
((2*n+4)/(5*n+7))^n*x^n
2^2
(3^(n+3))/(4^(n-1)*5^n)
Identical expressions
(sqrt(i- one)+sqrti)/(2n*sqrtn)
( square root of (i minus 1) plus square root of i) divide by (2n multiply by square root of n)
( square root of (i minus one) plus square root of i) divide by (2n multiply by square root of n)
(√(i-1)+√i)/(2n*√n)
(sqrt(i-1)+sqrti)/(2nsqrtn)
sqrti-1+sqrti/2nsqrtn
(sqrt(i-1)+sqrti) divide by (2n*sqrtn)
Similar expressions
(sqrt(i+1)+sqrti)/(2n*sqrtn)
(sqrt(i-1)-sqrti)/(2n*sqrtn)

Sum of series/ (sqrt(i-1)+sqrti)/(2n*sqrtn)

Sum of series (sqrt(i-1)+sqrti)/(2n*sqrtn)

The solution

You have entered [src]

  n                    
____                   
\   `                  
 \      _______     ___
  \   \/ i - 1  + \/ i 
   )  -----------------
  /             ___    
 /        2*n*\/ n     
/___,                  
i = 1

$$\sum_{i=1}^{n} \frac{\sqrt{i} + \sqrt{i - 1}}{\sqrt{n} 2 n}$$

Sum((sqrt(i - 1) + sqrt(i))/(((2*n)*sqrt(n))), (i, 1, n))

The answer [src]

  n                     
____                    
\   `                   
 \      ___     ________
  \   \/ i  + \/ -1 + i 
   )  ------------------
  /            3/2      
 /          2*n         
/___,                   
i = 1

$$\sum_{i=1}^{n} \frac{\sqrt{i} + \sqrt{i - 1}}{2 n^{\frac{3}{2}}}$$

Sum((sqrt(i) + sqrt(-1 + i))/(2*n^(3/2)), (i, 1, 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
```

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Identical expressions

Similar expressions

Sum of series (sqrt(i-1)+sqrti)/(2n*sqrtn)

The solution

Examples of finding the sum of a series