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Contents
Binomial Theorem
|
Binomial Theorem
for positive integral index
More Properties of the
Binomial Theorem
 General
(r + 1) th term in ascending powers of b,
nCr an-rbn
Finding
the middle term of the expansion (a + b)n,
if n
is even, there will be an odd numbers of terms.
the middle term is the 0.5 (n + 2) th term.
if n
is odd, there will be an even number of terms.
the middle terms are the 0.5 (n + 1) and 0.5 (n + 3) terms.
Finding
coefficients and term independent of x.
In the
expansion of
 ,
(i) find the coefficient of x5
(ii) find the term independent of x.
Find the general term
of the expansion:
coefficient of x5,
equate the power of x to 5.
30 - 5r = 5
r = 5
substitute value of r
back into the general term. ignore the part in x, only the coefficient of x5
is needed.
10C5
(0.5)5
= -7 7/8
term
independent of x, equate the power of x to 0.
30 - 5r = 0
r = 6
substitute r = 6 back into general term.
10C6
(0.5)6
= 3 9/32
The next page will deal with more
examples.
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