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Title: Binomial Theorem
Description: This notes include details about how the binomial theorem works. It includes: Properties of Binomial Coefficients, Series of Binomial Coefficients, General Term. All the further details are given in the PDF.
Description: This notes include details about how the binomial theorem works. It includes: Properties of Binomial Coefficients, Series of Binomial Coefficients, General Term. All the further details are given in the PDF.
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Binomial theorem
Properties of Binomial Coefficients
Series of Binomial Coefficients
1
...
3
...
5
...
7
...
This array is
called Pascal’s triangle
...
Since n is even, n
+ 1 is odd
...
If n is odd, then n + 1 is even
...
They are
term and
In the expansion of
[since 2n is even]
...
, where x ≠ 0, the middle term is
, i
...
, (n + 1)th term
which is a constant
...
Note: In the expansion of (a + b)n, rth term from the end = (n – r +2)th term from the beginning
Example 2: In the expansion of
, find the middle term and find the term which is
independent of x
...
e
...
Suppose (r + 1)th term
is independent of x
Title: Binomial Theorem
Description: This notes include details about how the binomial theorem works. It includes: Properties of Binomial Coefficients, Series of Binomial Coefficients, General Term. All the further details are given in the PDF.
Description: This notes include details about how the binomial theorem works. It includes: Properties of Binomial Coefficients, Series of Binomial Coefficients, General Term. All the further details are given in the PDF.