Question
The coefficient of $x^{n-1}$ in the expansion of $E=(2 x+1)^{n-1}+(2 x+1)^{n-2}(x+1)$$+\ldots+(x+1)^{n-1}$is(a) $2^{n}$(b) $2^{n}-1$(c) $2^{n}+1$(d) $2^{2 n}$
Step 1
We can see that this series is a geometric progression (GP) with common ratio $\frac{x+1}{2x+1}$. Show more…
Show all steps
Your feedback will help us improve your experience
Gaurav Kalra and 100 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The coefficient of $x^{n}$ in the expansion $(2 x+3)^{n}-$ $(2 x+3)^{n-1}(5-2 x)+(2 x+3)^{n-2}(5-2 x)^{2}+\ldots+(-1)^{n}$ $(5-2 x)^{n}$ is (A) $\frac{1}{8} 2^{n}$ (B) $(n+1) 2^{n}$ (C) $(n+1) 2^{n-3}$ (D) $-(n+1) 2^{n-2}$
If $|x|<1$, then the coefficient of $x^{n}$ in expansion of $(1$ $\left.+x+x^{2}+x^{3}+\ldots\right)^{2}$ is: (A) $n$ (B) $n-1$ (C) $n+2$ (D) $n+1$
In the expansion of $\left(x^{2}+1+\frac{1}{x^{2}}\right)^{n}, n \in \mathbf{N}$, (a) number of terms is $2 n+1$ (b) coefficient of constant term is $2^{n-1}$ (c) coefficient of $x^{2 x-2}$ is $n$ (d) coefficient of $x^{2}$ in $n$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD