Mister Exam

# Least common denominator n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2

An expression to simplify:

### The solution

You have entered [src]
  /       k    k                 k                   \     / k                  k\
n*\(1 + p)  + p *log(p) + (1 + p) *(k + 1)*log(1 + p)/   n*\p  + (k + 1)*(1 + p) /
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k                                           2
k            
$$- \frac{n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}} + \frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right)\right)}{k}$$
(n*((1 + p)^k + p^k*log(p) + ((1 + p)^k*(k + 1))*log(1 + p)))/k - n*(p^k + (k + 1)*(1 + p)^k)/k^2
General simplification [src]
  /   k     /       k    k                 k                   \          k        \
n*\- p  + k*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/ - (1 + p) *(1 + k)/
------------------------------------------------------------------------------------
2
k                                          
$$\frac{n \left(k \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right) - p^{k} - \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$
n*(-p^k + k*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p)) - (1 + p)^k*(1 + k))/k^2
n*((1.0 + p)^k + p^k*log(p) + (1.0 + p)^k*(1.0 + k)*log(1 + p))/k - n*(p^k + (1.0 + p)^k*(1.0 + k))/k^2
n*((1.0 + p)^k + p^k*log(p) + (1.0 + p)^k*(1.0 + k)*log(1 + p))/k - n*(p^k + (1.0 + p)^k*(1.0 + k))/k^2
Rational denominator [src]
   2 /       k    k                 k                   \       / k          k        \
n*k *\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/ - k*n*\p  + (1 + p) *(1 + k)/
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3
k                                           
$$\frac{k^{2} n \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right) - k n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{3}}$$
(n*k^2*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p)) - k*n*(p^k + (1 + p)^k*(1 + k)))/k^3
Common denominator [src]
     k            k        k                     k
- n*p  - n*(1 + p)  + k*n*p *log(p) + k*n*(1 + p) *log(1 + p)            k
------------------------------------------------------------- + n*(1 + p) *log(1 + p)
2
k                                                      
$$n \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \frac{k n p^{k} \log{\left(p \right)} + k n \left(p + 1\right)^{k} \log{\left(p + 1 \right)} - n p^{k} - n \left(p + 1\right)^{k}}{k^{2}}$$
(-n*p^k - n*(1 + p)^k + k*n*p^k*log(p) + k*n*(1 + p)^k*log(1 + p))/k^2 + n*(1 + p)^k*log(1 + p)
Combinatorics [src]
  /   k          k      k                   k               2        k           \
n*\- p  - (1 + p)  + k*p *log(p) + k*(1 + p) *log(1 + p) + k *(1 + p) *log(1 + p)/
----------------------------------------------------------------------------------
2
k                                         
$$\frac{n \left(k^{2} \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + k p^{k} \log{\left(p \right)} + k \left(p + 1\right)^{k} \log{\left(p + 1 \right)} - p^{k} - \left(p + 1\right)^{k}\right)}{k^{2}}$$
n*(-p^k - (1 + p)^k + k*p^k*log(p) + k*(1 + p)^k*log(1 + p) + k^2*(1 + p)^k*log(1 + p))/k^2
Trigonometric part [src]
  /       k    k                 k                   \     / k          k        \
n*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/   n*\p  + (1 + p) *(1 + k)/
------------------------------------------------------ - -------------------------
k                                           2
k            
$$\frac{n \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right)}{k} - \frac{n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$
n*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p))/k - n*(p^k + (1 + p)^k*(1 + k))/k^2
Powers [src]
  /       k    k                 k                   \     / k          k        \
n*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/   n*\p  + (1 + p) *(1 + k)/
------------------------------------------------------ - -------------------------
k                                           2
k            
$$\frac{n \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right)}{k} - \frac{n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$
n*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p))/k - n*(p^k + (1 + p)^k*(1 + k))/k^2
Combining rational expressions [src]
  /   k     /       k    k                 k                   \          k        \
n*\- p  + k*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/ - (1 + p) *(1 + k)/
------------------------------------------------------------------------------------
2
k                                          
$$\frac{n \left(k \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right) - p^{k} - \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$
n*(-p^k + k*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p)) - (1 + p)^k*(1 + k))/k^2
Assemble expression [src]
  /       k    k                 k                       k          k        \
|(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)   p  + (1 + p) *(1 + k)|
n*|-------------------------------------------------- - ---------------------|
|                        k                                       2         |
\                                                               k          /
$$n \left(\frac{p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}}{k} - \frac{p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}}{k^{2}}\right)$$
  /       k    k                 k                   \     / k          k        \
n*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/   n*\p  + (1 + p) *(1 + k)/
------------------------------------------------------ - -------------------------
k                                           2
k            
$$\frac{n \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right)}{k} - \frac{n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$
n*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p))/k - n*(p^k + (1 + p)^k*(1 + k))/k^2