تصاعد حسابی

${\displaystyle a_1{a}_2\cdots a_n=d^n{\left(\frac{a_1}{d}\right)}^{\overline{n}}=d^n\frac{\mathrm{\Gamma }\left(a_1/d+n\right)}{\mathrm{\Gamma }\left(a_1/d\right)},}$

${\displaystyle m\times (m+1)\times (m+2)\times \cdots \times (n-2)\times (n-1)\times n}$

${\displaystyle \frac{n!}{(m-1)!}.}$

${\displaystyle P_{50}=5^{50}\cdot \frac{\mathrm{\Gamma }\left(3/5+50\right)}{\mathrm{\Gamma }\left(3/5\right)}\approx 3.78438\times {10}^{98}}$

${\displaystyle a,(a+d),(a+2d),.................(a+(n-1)d)}$

${\displaystyle a(a+d)(a+2d)}$

${\displaystyle =(a^2+ad)(a+2d)}$

${\displaystyle a^n+n{a}^{n-1}{d}^{n-2}+(n-1)a^{n-2}{d}^{n-1}}$