Find the coefficient of $x$ in the binomial series for $\sqrt { 1 + x }$ .
A)2
B)-1
C)1
D) $- \frac { 1 } { 2 }$
E) $\frac { 1 } { 2 }$
F) $- \sqrt { 2 }$
G)-2

H) $\sqrt { 2 }$

Question

Find the coefficient of $x$ in the binomial series for $\sqrt { 1 + x }$ .
A)2
B)-1
C)1
D) $- \frac { 1 } { 2 }$ 
E) $\frac { 1 } { 2 }$ 
F) $- \sqrt { 2 }$ 
G)-2

H) $\sqrt { 2 }$

Quizplus · Accepted Answer

The binomial series for $\sqrt{1+x}$ can be written as $(1+x)^{1/2}$. The general term of the binomial expansion is given by $\binom{n}{k}x^k$, where $n$ is the exponent and $k$ is the term number. For the coefficient of $x$, we look at the term where $k=1$, which gives us $\binom{1/2}{1}x^1$. The binomial coefficient $\binom{1/2}{1} = \frac{1/2}{1} = \frac{1}{2}$, thus the coefficient of $x$ is $\frac{1}{2}$.

Find the Coefficient Of xxx In the Binomial Series For 1+x\sqrt { 1 + x }1+x​

Find the Coefficient Of $x$ In the Binomial Series For $\sqrt { 1 + x }$