List of top Mathematics Questions on Sequence and series asked in WBJEE

If \( a_1, a_2, \dots, a_n \) are in A.P. with common difference \( \theta \), then the sum of the series:
\[ \sec a_1 \sec a_2 + \sec a_2 \sec a_3 + \dots + \sec a_{n-1} \sec a_n = k (\tan a_n - \tan a_1), \]
where \( k = ? \)

The value of \(\lim_{n\rightarrow\infty}[(\frac{1}{2.3}+\frac{1}{2^2.3})+(\frac{1}{2^2.3^2}+\frac{1}{2^3.3^2})+.....+(\frac{1}{2^n.3^n}+\frac{1}{2^{n+1}.3^n})]\)

The sum of n terms of the following series; $1^3 + 3^3 + 5^3 + 7^3 + ....$ is

The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is

Let $S$ denote the sum of the infinite series $1+\frac{8}{2!}+\frac{21}{3!}+\frac{40}{4!}+\frac{65}{5!} ....... $. Then

The value of $1000\left[\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...... +\frac{1}{999\times1000}\right]$ is equal to

If $^nC_4,\, ^nC_5$ and $^nC_6$ are in $A.P.$, then $n$ is

The value of $\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+........$ is

For what value of $m$, $\frac{a^{m+1}+b^{m+1}}{a^{m}+b^{m}}$ is the arithmetic mean of $�a�$ and $�b�$ ?

If the $m^{th}$ term and the nth term of an $AP$ are respectively $\frac{1}{n}$ and $\frac{1}{m}$, then the $(mn )^{th}$ term of the $AP$ is

If $x=8+3\sqrt{7}$ and $xy=1,$ then the value of $\frac{1}{x^2}+\frac{1}{y^2}$ is

Let $Sn=\sum _{k=0}^1\frac{n}{n^2+kn+k^2}$ and $T_n=\sum _{k=0}^{1-1}\frac{n}{n^2+kn+k^2},$ for $n=1,2,3,\dots$ Then

Directions: The following question has four choices, out of which one or more are correct.The internal bisector of $\mathrm{\angle }A$ of a triangle $ABC$ meets side $BC$ at $D$. A line drawn through $D$ perpendicular to $AD$ intersects the side $AC$ at $E$ and side $AB$ at $F$. If $a,b$ and $c$ represent the sides of $\mathrm{\Delta }ABC$, then

The derivative of${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x=0$

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

If α and β are the roots of the equation x² + x + 1 = 0, then the equation whose roots are α¹⁹ and β⁷ is 

The order and degree of the differential equation ${(1+3{\mathrm{y}}_1)}^{\frac{2}{3}}$ respectively is:

If $\omega \ne 1$ is a cube root of unity, then the sum of the series $S=1+2\omega +3{\omega }^2+\dots \dots \dots +3n{\omega }^{3n}-1$ is

For the function f(x)= e^cosx , Rolle’s theorem is

If the sums of n terms of two arithmetic series are in the ratio 2n + 3 : 6n + 5, then the ratio between their 13^th terms is