(i) Prove that for any integers and , the ratio of two consecutive binomial…

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

(i) Prove that for any integers

n \ge 1

and

0 \le r \le n-1

, the ratio of two consecutive binomial coefficients satisfies

\frac{{^{\;n}C_{r+1}}}{{^{\;n}C_{r}}}=\frac{n-r}{r+1}.

(ii) Using the relation obtained in part (i), determine the least positive integer

r

for which

^{20}C_r\ge {^{20}C_{r+1}}.

(iii) Hence state the value(s) of

r

for which

{^{20}C_r}

attains its maximum value.