Binomial Theorem

Algebra Level 3

Consider the expansion of $(1+x)^{2n+1}$ : The sum of the coefficients of all the terms in the expansion is :

2^{2n-1}

2\cdot 4^{n}

4^{n-1}

None of the above

2 solutions

Parth Lohomi
Oct 10, 2015

Using binomial theorem we have

$(1+x)^{2n+1}= ^{2n+1}C_0 x^{2n+1} +^{2n+1}C_1 x^{2n}+^{2n+1}C_2 x^{2n-1}+......+^{2n+1}C_{2n+1} x^0$

We desire to find $\sum_{r=0}^{2n+1}$ $^{2n+1} C_r$

So we Put $x=1$ So.,

$(1+(1))^{2n+1}=\sum_{r=0}^{2n+1}$ $^{2n+1}C_r$ $=2^{2n+1}=2\times 2^{2n}=2\times 4^n$

Thats too easy, it should not be level 4.

siddharth bhatt - 5 years, 8 months ago

I think question is a bit overrated

Atul Shivam - 5 years, 8 months ago

just put x 1

Dev Sharma - 5 years, 8 months ago

Atul Shivam
Oct 10, 2015

Simply put x=1 and calculate it