Maths important formula - BINOMIAL THEOREM

BINOMIAL THEOREM

1.Statement of Binomial Theorem:

if $a,b\, \in \, R\, \, \, and\, n\, \in \, R\, then$

${(a+b)}^{n}={^{n}_{\, }{C}_{0}{a}^{n}{b}^{0}+}{^{n}_{\, }{C}_{1}{a}^{n-1}{\, b}^{1}+{^{n}_{\, }{C}_{2}}}{a}^{n-2}{b}^{2}+.................+{^{n}_{\, }{C}_{n}}{a}^{0}{b}^{n}=\sum ^{n}_{r=0} {^{n}_{\, }{C}_{r}{a}^{n-r}{b}^{r}}$

2. Properties of Binomial Theorem:

i. General term :

${T}_{r+1}={^{n}_{\, }{C}_{r}{a}^{n-r}{b}^{r}}$

ii. middle term(s):

a. if n is even, there is only one middle term which is $(\frac {n+2} {2})th\,$ term.

b. if n is odd, there are two middle terms which are $(\frac {n+1} {2})th$ and $(\frac {n+1} {2}+1)th$ term

3.Multinomial Theorem :

Multinomial Theorem :

Here total number of terms in the expansions = ${^{n+k-1}_{\, }{C}_{k-1}}$

4. Application of Binomial Theorem:

if ${(\sqrt {A}+B)}^{n}=I+f$ where I and n are positive intergers, n beign odd and 0 < f <1 then

$"(I+f)f\,$

if n is an even integer, then (I+f)(I - f )= k^n

5. Properties of Binomial Coefficients :

Post By : Preeti Rai 13 Apr, 2020 272 views Maths

Maths important formula - BINOMIAL THEOREM

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