1. Tardigrade
  2. Question
  3. Mathematics
  4. The total number of terms in the expansion of ( 1 + x ) 2n - ( 1 - x ) 2n after simplification is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The total number of terms in the expansion of $ ( 1 + x ) ^{2n} - ( 1 - x ) ^{2n} $ after simplification is

AMUAMU 2012Binomial Theorem

Solution:

$(1+x)^{2 n}-(1-x)^{2 n} $
$=\left({ }^{2 n} C_{0}+{ }^{2 n} C_{1} x+{ }^{2 n} C_{2} x^{2}++{ }^{2 n} C_{2 n} x^{2 n}\right) $
$-\left({ }^{2 n} C_{0}-{ }^{2 n} C_{1} x+{ }^{2 n} C_{2} x^{2}-{ }^{2 n} C_{3} x^{3}\right. $
$\left.+(-1)^{n}\,{ }^{2 n} C_{2 n} x^{2 n}\right) $
$=2\left\{{ }^{2 n} C_{1} x+{ }^{2 n} C_{3} x^{3}++{ }^{2 n} C_{2 n-1}(x)^{2 n-1}\right\}$
Hence, total number of terms is $n$.