Greates Binomial coefficient(or Middle terms)
(1) If n is even, then there is only one middle term which (h/2 + 1) th
+ 1 = n
is greatest bionomial coefficient
(2) If n is each them trere are two middle terms which are th
are greatest bionoimial ccoefficients
Numarically Greatest term of Bionmial expansion
(a + x)n
= Co an
The numerically greatest term will be Tr+1
where r = ....
itself is a natural number then Tr
both are numerically greatest terms.
for given a, x and n
Show that middle term in the expansion of (1 + x)2n
is img........... where n isa +ve integer.
This number of terms in expassion of (1 + x)2n
is 2n + 1 (odd)
So, its middle term is (n + 1)th
Required Term = Tn+1
find the greatest term in the expansion of
Let us find r =
So, r =
is greatest term
Summation of series of Bionomial co-efficients
Series of Bionomia cofficients cn be umme by uing methods like by taaking prouct o expnion of two bionomial by differentiating bionomial expansion, integraating bionomial expansion by equating real and imaginory part of a eries etc.
(1) Sum of sevies by taking product o expnsions of two bionomials if we find the product of binomial coefficients in tnhe sevies then this method can be used .