Question

answer this question please

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Answer 1

Answer:

Step-by-step explanation:

We have,

$\displaystyle\sf{\,^{n}C_{n-1}+\,^{n}C_{n-2}}$

$\displaystyle\sf{=\dfrac{n!}{(n-1)!(n-(n-1))!}+\dfrac{n!}{(n-2)!(n-(n-2))!}}$

$\displaystyle\sf{=\dfrac{n!}{(n-1)!(n-n+1)!}+\dfrac{n!}{(n-2)!(n-n+2)!}}$

$\displaystyle\sf{=\dfrac{n!}{(n-1)!(1)!}+\dfrac{n!}{(n-2)!(2)!}}$

$\displaystyle\sf{=\dfrac{n(n-1)!}{(n-1)!(1)!}+\dfrac{n(n-1)(n-2)!}{(n-2)!(2)!}}$

$\displaystyle\sf{=\dfrac{n}{1}+\dfrac{n(n-1)}{2}}$

$\displaystyle\sf{=n+\dfrac{n^2-n}{2}}$

$\displaystyle\sf{=\dfrac{2n+n^2-n}{2}}$

$\displaystyle\sf{=\dfrac{n^2+n}{2}}$

$\displaystyle\sf{=\dfrac{n(n+1)}{2}}$