Grove HSC 3U EX10.4 Q15

WORKSHEET 26.1 Q6c

Thx Holly

WORKSHEET 26.1 Q6b

WORKSHEET 26.1 Q4a

WORKSHEET 26.1 Q3a

GROVE HSC 3U EX10.3, Q5a

GROVE HSC 3U EX10.3, Q11

Thx POPPY :-)

GROVE HSC 3U EX10.3, Q10

EX 26.1 Worksheet Q6b

Thx Camille :-)

GROVE HSC 3U EX10.4 BINOMIAL COEFFICIENTS, FIND CONSTANT TERM

GROVE HSC 3U EX10.4 BINOMIAL COEFFICIENTS, FIND CONSTANT TERM

Thx Becster :-)

Grove HSC 3U book EX 10.1 Q15 Pascal Triangle identity

Prove $\left({n\atop k}\right)=\left({n-1\atop k-1}\right)+\left({n-1\atop k}\right)$


LHS $=\left({n\atop k}\right)={n!\over k! (n-k)!}$

RHS $=\left( {n-1\atop k-1}\right)+\left({n-1 \atop k}\right)$

$={(n-1)!\over (k-1)! (n-1-(k-1))!}+ {(n-1)!\over k! (n-1-k)!}$

$={(n-1)!\over (k-1)! (n-k)!}+ {(n-1)!\over k! (n-k-1)!}$

$={k(n-1)!\over k(k-1)! (n-k)!}+ {(n-1)!(n-k)\over k! (n-k)(n-k-1)!}$

$={k(n-1)!\over k! (n-k)!}+ {(n-1)!(n-k)\over k! (n-k)!}$

$={k(n-1)! + (n-1)!(n-k)\over k! (n-k)!}$

$={(n-1)!(k + (n-k))\over k! (n-k)!}$

$={(n-1)!n\over k! (n-k)!}$

$={n!\over k! (n-k)!}$

=LHS

as required.

FACTORISE $K! + (K+1)! $

FACTORISE 

$K! + (K+1)!$

$=  K!  +   (K+1)K!$

$= K!  (1 + K + 1)$

$= K! (K+2)$