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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
Общий знаменатель 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
Решение
Вы ввели
[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) /
------------------------------------------------------ - -------------------------
k 2
k
$$- \frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} + p^{k}\right)}{k^{2}} + \frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right)}{k}$$
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)
Общее упрощение
[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
$$\frac{n \left(k \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right) - \left(k + 1\right) \left(p + 1\right)^{k} - p^{k}\right)}{k^{2}}$$
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
Рациональный знаменатель
[src]
k k k k
k n*p n*(1 + p) n*p *log(p) n*(1 + p) *log(1 + p)
n*(1 + p) *log(1 + p) - ---- - ---------- + ----------- + ---------------------
2 2 k k
k k
$$n \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \frac{n p^{k} \log{\left(p \right)}}{k} + \frac{n \left(p + 1\right)^{k} \log{\left(p + 1 \right)}}{k} - \frac{n p^{k}}{k^{2}} - \frac{n \left(p + 1\right)^{k}}{k^{2}}$$
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)/
---------------------------------------------------------------------------------------
3
k
$$\frac{k^{2} n \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right) - k n \left(\left(k + 1\right) \left(p + 1\right)^{k} + p^{k}\right)}{k^{3}}$$
(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
Комбинаторика
[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
Степени
[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
$$\frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right)}{k} - \frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} + p^{k}\right)}{k^{2}}$$
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
Собрать выражение
[src]
k k / 2 \
n*p *(-1 + k*log(p)) + n*(1 + p) *\-1 + k*log(1 + p) + k *log(1 + p)/
---------------------------------------------------------------------
2
k
$$\frac{n p^{k} \left(k \log{\left(p \right)} - 1\right) + n \left(p + 1\right)^{k} \left(k^{2} \log{\left(p + 1 \right)} + k \log{\left(p + 1 \right)} - 1\right)}{k^{2}}$$
/ 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 /
$$n \left(\frac{\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}}{k} - \frac{\left(k + 1\right) \left(p + 1\right)^{k} + p^{k}}{k^{2}}\right)$$
/ 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
$$\frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right)}{k} - \frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} + p^{k}\right)}{k^{2}}$$
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
Общий знаменатель
[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)
Объединение рациональных выражений
[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
$$\frac{n \left(k \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right) - \left(k + 1\right) \left(p + 1\right)^{k} - p^{k}\right)}{k^{2}}$$
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
Численный ответ
[src]
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