$\sum _{r=1}^n\frac{r^2-r-1}{\left(r+1\right)!}$ is equal to

Important Questions on Sequence and Series

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 101

Solution set for ${\left(\sqrt{2+\sqrt{2}}\right)}^x+{\left(\sqrt{2-\sqrt{2}}\right)}^x=2·2^{\frac{x}{4}}$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 102

If $x^2-\left(a+b+c\right)x+\left(ab+bc+ca\right)=0$ has imaginary roots, where $a,b,c\in R^{+}$, then $\sqrt{a},\sqrt{b}$ and $\sqrt{c}$

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 103

If first three terms of a sequence $\frac{1}{16},a,b,\frac{1}{6}$ are in geometric series and the last three terms are in harmonic series, then the values of $a$ and $b$ will be

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 104

If the roots of the equation $a\left(b-c\right)x^2+b\left(c-a\right)x+c\left(a-b\right)=0$ are equal, then $a,b$ and $c$ are in

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 105

If $\mathrm{A}.\mathrm{M}$ between two numbers is $5$ and their $\mathrm{G}.\mathrm{M}$ is $4$, then the $\mathrm{H}.\mathrm{M}$ will be

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 106

If $\log \left(a+c\right),\log \left(c-a\right)$ and $\log \left(a-2b+c\right)$ are in $\mathrm{AP}$, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 107

If $\cos \left(x-y\right),\cos x$ and $\cos \left(x+y\right)$ are in $\mathrm{HP}$, then $\cos x\sec \left(\frac{y}{2}\right)$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Target Exercises>Q 108

${\log }_{3}2,{\log }_{6}2$ and ${\log }_{12}2$ are in