Download App

8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
$\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ........ + .......\frac{1}{{n.(n + 1)}}$ equals
  • A
    $\frac{1}{{n(n + 1)}}$
  • ✓
    $\frac{n}{{n + 1}}$
  • C
    $\frac{{2n}}{{n + 1}}$
  • D
    $\frac{2}{{n(n + 1)}}$
✓

Answer

Correct option: B.
$\frac{n}{{n + 1}}$
b
(b) $\left( {\frac{1}{1} - \frac{1}{2}} \right) + \left( {\frac{1}{2} - \frac{1}{3}} \right) + \left( {\frac{1}{3} - \frac{1}{4}} \right) + ......... + \left( {\frac{1}{n} - \frac{1}{{n + 1}}} \right)$

$ = 1 - \frac{1}{{n + 1}} = \frac{n}{{n + 1}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 8. sequence and series→8. sequence and series — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Co-efficient of $\alpha ^t$ in the expansion of,

$(\alpha + p)^{m - 1} + (\alpha + p)^{m - 2} (\alpha + q) + (\alpha + p)^{m - 3} (\alpha + q)^2 + ...... (\alpha + q)^{m - 1}$

where $\alpha \ne - q$ and $p \ne q$ is :

→
The radical centre of the circles ${x^2} + {y^2} - 16x + 60 = 0,\,{x^2} + {y^2} - 12x + 27 = 0,$ ${x^2} + {y^2} - 12y + 8 = 0$ is
→
The coordinates of the point $A$ and $B$ are $(ak,0)$ and $\left( {\frac{a}{k},0} \right),\,\,(k = \pm 1)$. If a point $P$ moves so that $PA = kPB,$ then the equation to the locus of $P$ is
→
The value of $\lambda$ for which the lines $3\text{x} + 4\text{y} = 5, 5\text{x} + 4\text{y} =4$ and $\lambda\text{x} + 4\text{y} = 6$ meet at a point is:
→
The graph of the conic $x^2-(y-1)^2=1$ has one tangent line with positive slope that passes through the origin. The point of the tangency being $(a, b)$ then find the value of $\sin ^{-1}\left(\frac{a}{b}\right)$
→
Find the distance between (12, 3, 4) and (4, 5, 2):
→
If $|x|\, < 1$, then the sum of the series $1 + 2x + 3{x^2} + 4{x^3} + ...........\infty $ will be
→
Let the mean of the data

$X$ $1$ $3$ $5$ $7$ $9$
$(f)$ $4$ $24$ $28$ $\alpha$ $8$

be $5.$ If $m$ and $\sigma^2$ are respectively the mean deviation about the mean and the variance of the data, then $\frac{3 \alpha}{m+\sigma^2}$ is equal to $..........$.

→
The function $f(x) = \sin \frac{{\pi x}}{2} + 2\cos \frac{{\pi x}}{3} - \tan \frac{{\pi x}}{4}$ is period with period
→
$\frac{{{1^3} + {2^3} + {3^3} + {4^3} + {{........12}^3}}}{{{1^2} + {2^2} + {3^2} + {4^2} + {{.........12}^2}}} = $
→