Particular Terms for Fractional Index

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 cases, we begin by evaluating the general term T_r+1 and then finding the value of r by assuming T_r+1 to be the required term.

Working rules for finding particular terms:

Step 1:

In the expansion of (1+x)ⁿ, the (r+1)th term is equal to

Step 2:

Find the general terms T_r+1 in the expansion of (1+x)ⁿ.

Step 3:

Assume that T_r+1 is the desired particular term.

Step 4:

Find the value of r.

Step 5:

Put the value of r in the term T_r+1. This gives the required particular term(s).

Example:

Suggested answer:

T_r+1 in the expansion of

Putting r = 8, we get coefficient of

Putting r = 9, we get coefficient of