The-first-three-terms-in-the-binomial-expansion-p-q-m-in-ascending-order-of-q-are-denoted-by-a-b-and-c-respectively-Show-that-b-2-ac-2m-m-1-

Question Number 118759 by ZiYangLee last updated on 19/Oct/20

The first three terms in the binomial expansion

{(p - q)}^{m}, in ascending order of q, are denoted

by a, b and c respectively .

Show that \frac{b^{2}}{a c} = \frac{2 m}{m - 1}

Commented by PRITHWISH SEN 2 last updated on 19/Oct/20

a = p^{m}

b = {mp}^{m - 1} . (- q)

c = \frac{m (m - 1)}{2} p^{m - 2} . q^{2}

\frac{b^{2}}{ac} = \frac{m^{2} p^{2 m - 2} . q^{2}}{p^{m} . \frac{m (m - 1)}{2} p^{m - 2} . q^{2}} = \frac{2 m}{m - 1} proved

Commented by ZiYangLee last updated on 19/Oct/20

b = {m p}^{m - 1} \cdot (- q)

Commented by PRITHWISH SEN 2 last updated on 19/Oct/20

yes

Commented by ZiYangLee last updated on 22/Oct/20

★