Expansions for Positive Integral Index
Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..
Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or o..
Particular Terms for Positive Integral Index
Particular Terms for Positive Integral Index - Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a tedious task, speci..
Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or od..
Greatest Terms for Positive Integral Index
In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r+1 remains greater tha..
In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r+1 remains greater tha..Some particular expansions for Positive Integral Index
Working rules for expanding (a + b) n n N: Step 1: The value of index, n implies that there will be n+1 terms in the expansion of (a + b) n . Step 2: Write the first term: n C 0 a n b 0 . Step 3: For the second term, take coefficient as n C 1 , decreases the po..
Some particular expansions for Positive Integral Index
For n N, we have: a) (a - b) n (a +(- b))..
For n N, we have: a) (a - b) n (a +(- b))..Particular Terms for Positive Integral Index
Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a tedious task, specially when the index n is large. In such cases, we begin b..
Binomial Theorem Application for Positive Integral Index
Theorem - Using Binomial theorem, prove tha..
Theorem - Using Binomial theorem, prove tha..Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method)
We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the factors, we get the term a n..
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