Formula termenului general este:
[tex]T_{k+1}=C_n^ka^{n-k}b^k[/tex]
În cazul nostru, [tex]n=13,~a=a,~iar~b= -\dfrac{1}{a} [/tex].
Al 10-lea termeni va fi:
[tex]T_{10}=T_{9+1}=C_{13}^9a^{13-9}\cdot(- \dfrac{1}{a} )^9\\\\
T_{10}=-C_{13}^9 a^4\cdot a^{-9} \\\\
T_{10}=- \dfrac{13!}{9!(13-9)!}\cdot a^{4-9}\\\\
T_{10}=- \dfrac{13!}{9!\cdot4!}\cdot a^{-5} \\\\
T_{10}=- \dfrac{9!\cdot10\cdot11\cdot12\cdot13}{9!\cdot1\cdot2\cdot3\cdot4} \cdot \dfrac{1}{a^5}[/tex]
Prin simplificări se ajunge la rezultatul:
[tex]T_{10}=- \dfrac{715}{a^5} [/tex]
