Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

The sum of coefficients of odd powers of $x$ in the expansion $(1+x)^{50}$ is ?

$\begin{array}{1 1} 0 \\ 2^{49} \\ 2^{50} \\ 2^{51} \end{array}$

Can you answer this question?

1 Answer

0 votes
$=(^nC_0+^nC_2x^2+^nC_4+......)$ - $(^nC_1x+^nC_3x^3+^nC_5x^5+........)$
Take $x=1,\:\:and\:\:n=50$ in $(i)$
$i.e.,$$ 2^{50}=$ (sum of coeff. of odd powers of $x$)+(sum of coeff. of even powers of $x$
Similarly by taking $x=1,n=50$ in $(ii)$
$0$=(Sum of coeff. of odd powers)-(sum of coeff. of even powers)
$\Rightarrow\:$sum of coeff. of odd powers = sum of coeff. of even powers.
$\therefore 2^{50}=2$(sum of coeff. of odd powers)
$\Rightarrow\:$Sum of coeff. of odd powers =$ 2^{49}$


answered Sep 24, 2013 by rvidyagovindarajan_1
edited Dec 24, 2013 by meenakshi.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App