general term for fractional index

The General Term for Fractional Index is:..

For n Q and |x|<1, we have ...

Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (1+x) n . This can be done by expanding (1+x) n to certain terms and then locating the required term. Generally this becomes a tedious task. In such c..

General Term for Positive Integral Index is: For 0 r n, we have T r + 1 = n C r a n - r b r..

For n N, we have . Let T r + 1 (0 r n) be the (r+1) t h term in the expansio..

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..

Binomial Theorem for Fractional Index - For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides with that as given ea..

>This is the same expansion as would have given by the binomial theorem for positive integral index..

For n Q, we have: ..

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..