MCQ
If $|x| > 1$, then ${(1 + x)^{ - 2}}$ =
- A$1 - 2x + 3{x^2} - ....$
- B$1 + 2x + 3{x^2} + $....
- C$1 - \frac{2}{x} + \frac{3}{{{x^2}}} - ....$
- ✓$\frac{1}{{{x^2}}} - \frac{2}{{{x^3}}} + \frac{3}{{{x^4}}} - $...
✓
Answer
Correct option: D.
$\frac{1}{{{x^2}}} - \frac{2}{{{x^3}}} + \frac{3}{{{x^4}}} - $...
d
(d) Given that $|x|>1.$
(d) Given that $|x|>1.$
So given expression can be written as
${x^{ - 2}}{\left( {1 + \frac{1}{x}} \right)^{ - 2}} = {x^{ - 2}}\left[ {1 - \frac{2}{x} + \frac{3}{{{x^2}}} - \frac{4}{{{x^3}}} + ....} \right]$
$ = \left[ {\frac{1}{{{x^2}}} - \frac{2}{{{x^3}}} + \frac{3}{{{x^4}}} - \frac{4}{{{x^5}}} + ....} \right]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The volume of spherical cap of height $h$ cut off from a sphere of radius $a$ is equal to
→Let the function $f :[0,2] \rightarrow R$ be defined as$f(x)=\left\{\begin{array}{cc}e^{\min \left[x^2, x-[x]\right\}}, & x \in[0,1) \\e^{\left[x \log _e x\right]}, & x \in[1,2]\end{array}\right.$ where $[t]$ denotes the greatest integer less than or equal to $t.$ Then the value of the integral $\int \limits_0^2 x f(x) d x$ is
→The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-
→If $(20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots \ldots$. $+20(21)^{19}= k (20)^{19}$, then $k$ is equal to
→If a circular iron sheet of radius $30\,cm$ is heated such that its area increases at the uniform rate of $6\pi \,\,cm^2/hr,$ then the rate (in $cm/hr$ ) at which the radius of the circular sheet increases is
→How many $3 \times 3$ matrices $\mathrm{M}$ with entries from $\{0,1,2\}$ are there, for which the sum of the diagonal entries of $M^T M$ is $5$ ?
→If $A$ and $B$ are disjoint, then $n(A \cup B)$ is equal to
→The lines $ax + by + c = 0$, where $3a + 2b + 4c = 0$ are concurrent at the point
→$\int_{}^{} {\frac{{{x^2} - 1}}{{{x^4} + {x^2} + 1}}\;dx = } $
→ $(i)$ $f (x)$ is continuous and defined for all real numbers
→$(ii)$ $f '(-5) = 0 \,; \,f '(2)$ is not defined and $f '(4) = 0$
$(iii)$ $(-5, 12)$ is a point which lies on the graph of $f (x)$
$(iv)$ $f ''(2)$ is undefined, but $f ''(x)$ is negative everywhere else.
$(v)$ the signs of $f '(x)$ is given below
On the possible graph of $y = f (x)$ we have 