Question

Cn+1^7 -Cn^7 =Cn^8 则n等于多少

Answer 1

C(n+1 7) -C(n 7)=C(n 8)

(n+1)n(n-1)...(n-5)/(1×2×...×7)- n(n-1)...(n-6)/(1×2×...×7)=n(n-1)...(n-7)/(1×2×...×8)

等式两边同乘以(1×2×...×8)/[n(n-1)...(n-5)]

8(n+1)-8(n-6)=(n-6)(n-7)

整理,得

n²-13n-14=0

(n+1)(n-14)=0

n=-1(舍去)或n=14

n=14