Mister Exam

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Sum of series:
(1-x^4)^n/(n+2)
a^n*cos(a)+b^n*sin(n*b)
factorial(6*n)/4^n
3.8
Identical expressions
(one hundred !)/(n!*(one hundred -n)!)*((zero . one hundred and twenty-five)^n)*((one - zero . one hundred and twenty-five)^(one hundred -n))
(100!) divide by (n! multiply by (100 minus n)!) multiply by ((0.0125) to the power of n) multiply by ((1 minus 0.0125) to the power of (100 minus n))
(one hundred !) divide by (n! multiply by (one hundred minus n)!) multiply by ((zero . one hundred and twenty minus five) to the power of n) multiply by ((one minus zero . one hundred and twenty minus five) to the power of (one hundred minus n))
(100!)/(n!*(100-n)!)*((0.0125)n)*((1-0.0125)(100-n))
100!/n!*100-n!*0.0125n*1-0.0125100-n
(100!)/(n!(100-n)!)((0.0125)^n)((1-0.0125)^(100-n))
(100!)/(n!(100-n)!)((0.0125)n)((1-0.0125)(100-n))
100!/n!100-n!0.0125n1-0.0125100-n
100!/n!100-n!0.0125^n1-0.0125^100-n
(100!) divide by (n!*(100-n)!)*((0.0125)^n)*((1-0.0125)^(100-n))
Similar expressions
(100!)/(n!*(100-n)!)*((0.0125)^n)*((1-0.0125)^(100+n))
(100!)/(n!*(100+n)!)*((0.0125)^n)*((1-0.0125)^(100-n))
(100!)/(n!*(100-n)!)*((0.0125)^n)*((1+0.0125)^(100-n))

Sum of series/ (100!)/(n!*(100-n)!)*((0.0125)^n)*((1-0.0125)^(100-n))

Sum of series (100!)/(n!(100-n)!)((0.0125)^n)*((1-0.0125)^(100-n))

The solution

You have entered [src]

 100                                     
 ___                                     
 \  `                                    
  \        100!           n       100 - n
   )  -------------*0.0125 *0.9875       
  /   n!*(100 - n)!                      
 /__,                                    
n = 1

$$\sum_{n=1}^{100} 0.9875^{100 - n} 0.0125^{n} \frac{100!}{n! \left(100 - n\right)!}$$

Sum(((factorial(100)/((factorial(n)*factorial(100 - n))))*0.0125^n)*0.9875^(100 - n), (n, 1, 100))

The rate of convergence of the power series

The answer [src]

0.715743483304891

$$0.715743483304891$$

0.715743483304891

Numerical answer [src]

0.715743483304890897327499223544

0.715743483304890897327499223544

The graph

Sum of series (100!)/(n!*(100-n)!)*((0.0125)^n)*((1-0.0125)^(100-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 (100!)/(n!*(100-n)!)*((0.0125)^n)*((1-0.0125)^(100-n))

The solution

Examples of finding the sum of a series

Sum of series (100!)/(n!(100-n)!)((0.0125)^n)*((1-0.0125)^(100-n))