_ m = 1 ^n m^2 is equal to - Vidyadip

MCQ

$\sum\limits_{m = 1}^n {{m^2}} $ is equal to

A
$\frac{{m(m + 1)}}{2}$
B
$\frac{{m(m + 1)(2m + 1)}}{6}$
✓
$\frac{{n(n + 1)(2n + 1)}}{6}$
D
$\frac{{n(n + 1)}}{2}$

✓

Answer

Correct option: C.

$\frac{{n(n + 1)(2n + 1)}}{6}$

c
(c) It is nothing but $\sum n^2$ $= \frac{{n(n + 1)(2n + 1)}}{{6}}$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Number of positive solution of the equation,$\int\limits_0^x {\,\,{{\left( {t\,\, - \,\,\left\{ t \right\}} \right)}^2}}$ $dt = 2 (x - 1)$ where $\{ \}$ denotes the fractional part function is :

Let $\vec a = 2\hat i + \hat j - 2\hat k$ and $\vec b = \hat i + \hat j$ . Let $\vec c$ be vector such that $\left| {\vec c - \vec a} \right| = 3,\;\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right| = 3$ and the angle between $\vec c$ and $\vec a \times \vec b$ be $30^\circ $ . Then $\vec a \cdot \vec c$ is equal to :

The number of integral terms in the expansion of ${\left( {\sqrt 3 + \sqrt[8]{5}} \right)^{256}}$ is

For the system of linear equations

$2 x-y+3 z=5$

$3 x+2 y-z=7$

$4 x+5 y+\alpha z=\beta$

Which of the following is NOT correct ?

Let $y = g (x)$ be the inverse of a bijective mapping $f : R \rightarrow R \, f (x) = 3x^3 + 2x. $ The area bounded by the graph of $g (x),$ the $x-$ axis and the ordinate at $x = 5$ is :

If the line $2x + 3ay - 1 = 0$ and $3x + 4y + 1 = 0$ are mutually perpendicular, then the value of $a$ will be

$6$ points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original $6$ points). The number of distinct points of intersection is equal to

$x = 1 + a + {a^2} + ....\infty \,(a < 1)$ $y = 1 + b + {b^2}.......\infty \,(b < 1)$ Then the value of $1 + ab + {a^2}{b^2} + ..........\infty $ is

In a square matrix $A$ of order $3, a_{i i} = m_i + i$ where $i = 1, 2, 3 $ and $m_i's$ are the slopes (in increasing order of their absolute value) of the $3 $ normals concurrent at the point $(9, - 6)$ to the parabola $ y^2 = 4x$ . Rest all other entries of the matrix are one. The value of $det\,(A)$ is equal to

The area bounded by the straight lines $x = 0,x = 2$ and the curves $y = {2^x},y = 2x - {x^2}$ is