Assertion $(A)$: If $|x| < 1$,then $\sum_{n=0}^{\infty}(-1)^n x^{n+1} = \frac{x}{x+1}$.
Reason $(R)$: If $|x| < 1$,then $(1+x)^{-1} = 1-x+x^2-x^3+\dots$.
Which one of the following is true?
Reason $(R)$: If $|x| < 1$,then $(1+x)^{-1} = 1-x+x^2-x^3+\dots$.
Which one of the following is true?
- A$A$ and $R$ are true,$R$ is a correct explanation of $A$.
- B$A$ and $R$ are true but $R$ is not a correct explanation of $A$.
- C$A$ is true,but $R$ is false.
- D$A$ is false,but $R$ is true.
Explore More
Similar Questions
If $|x| > 1$,then $(1 + x)^{-2} = $
Difficult
View SolutionIf $x$ is positive,the first negative term in the expansion of $(1 + x)^{27/5}$ is
DifficultAIEEE 2003
View SolutionAssuming $|x|$ to be so small that $x^2$ and higher powers of $x$ can be neglected,then $\frac{\sqrt{1+x}+(1-x)^{3/2}}{(1+x)+\sqrt{1+x}} = $
If $x$ is a positive real number and the first negative term in the expansion of $(1+x)^{27/5}$ is $t_k$,then $k=$
The expansion of $(1+x+x^2)^{-3/2}$ in powers of $x$ is valid if
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo