JAMB - Mathematics (2012 - No. 36)
Evaluate n+1Cn-2 If n =15
3630
3360
1120
560
Vysvětlení
\(\frac{n + 1 (n - 2)}{(n + 1)!}\)
\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)
\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)}{3!}\)
Since n = 15
\(\frac{(15 + 1)(15)(15-1)}{3!}\)
\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)
= 560
\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)
\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)
\(\frac{(n + 1)(n)(n-1)}{3!}\)
Since n = 15
\(\frac{(15 + 1)(15)(15-1)}{3!}\)
\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)
= 560