Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

Find the Term Independent of X in the Expansion of the Expression: (Vi) ( X − 1 X 2 ) 3 N - Mathematics

Find the term independent of x in the expansion of the expression: 

(vi)  \[\left( x - \frac{1}{x^2} \right)^{3n}\]

 

Advertisement Remove all ads

Solution

(vi)  Suppose the (r + 1)th term in the given expression is independent of x.
Now, 

\[\left( x - \frac{1}{x^2} \right)^{3n} \]
\[ T_{r + 1} = ^{3n}{}{C}_r x^{3n - r} \left( \frac{- 1}{x^2} \right)^r \]
` = ( - 1 )^r "^(3n) C_r x^{3n - r - 2r} `
\[\text{ For this term to be independent of x, we must have} \]
\[3n - 3r = 0\]
\[ \Rightarrow r = n\]
\[\text{ Hence, the required term is the (n + 1)th term .}  \]
\[\text{ Now, we have} \]
`( - 1 )^n "^3n C_n`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 16.06 | Page 39
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×