Cevap:
26
Adım adım açıklama:
[tex]\frac{(n+5)!}{(n+3)!} =\frac{(n+5)(n+4)(n+3)!}{(n+3)!} =(n+5)(n+4)=n^2+9n+20[/tex]
[tex]\frac{(n+4)!}{(n+2)!} =\frac{(n+4)(n+3)(n+2)!}{(n+2)!} =(n+4)(n+3)=n^2+7n+12[/tex]
Bunları toplarsak;
[tex]n^2+9n+20+n^2+7n+12=2n^2+16n+32[/tex]
ve
[tex]2n^2+16n+32=1800\\\\n^2+8n+16=900\\\\(n+4)^2=900\\\\n+4=30\\\\n=26[/tex]
