JEE Mains · Maths · STD 11 - 12. limits
The value of \(\lim _{n \rightarrow \infty}\left(\sum_{k=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}\right)\) is:
- A \(4 / 3\)
- B 2
- C \(7 / 3\)
- D \(5 / 3\)
Answer & Solution
Correct Answer
(D) \(5 / 3\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!} \) \( =\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{k^3+6 k^2+11 k+6-1}{(k+3)!} \) \( =\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{(k+1)(k+2)(k+3)-1}{(k+3)!} \)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\lim \limits_{x \rightarrow 1}\left(\frac{\int \limits_{0}^{(x-1)^{2}} \operatorname{tcos}\left(t^{2}\right) d t}{(x-1) \sin (x-1)}\right)\) is equal toJEE Mains 2020 Hard
- An unbiased coin is tossed \(5\) times. Suppose that a variable \(\mathrm{X}\) is assigned the value \(\mathrm{k}\) when \(\mathrm{k}\) consecutive heads are obtained for \(\mathrm{k}=3,4,5\) otherwise \(X\) takes the value \(-1 .\) Then the expected value of \(X,\) isJEE Mains 2020 Hard
- The sum of all the elements in the set \(\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid\) \(H.C.F.\) of \(n\) and \(2040\) is \(1\,\}\) is equal to \(.....\)JEE Mains 2021 Hard
- Let \(w _1\) be the point obtained by the rotation of \(z_1=5+4 i\) about the origin through a right angle in the anticlockwise direction, and \(w_2\) be the point obtained by the rotation of \(z_2=3+5 i\) about the origin through a right angle in the clockwise direction. Then the principal argument of \(w _1- w _2\) is equal to \(...........\).JEE Mains 2023 Hard
- The number of words, with or without meaning, that can be formed using all the letters of the word \(ASSASSINATION\) so that the vowels occur together, is \(.............\).JEE Mains 2023 Hard
- A vector \(\vec n\) is inclined to \(x-\) axis at \(45^o\), to \(y-\) axis at \(60^o\) and at an acute angle to \(z-\) axis. If \(\vec n\) is a normal to a plane passing through the point \(\left( {\sqrt 2 , - 1,1} \right)\) then the equation of the plane isJEE Mains 2013 Hard
More PYQs from JEE Mains
- The area of the triangle with vertices \(A ( z ), B ( iz )\) and \(C(z+i z)\) isJEE Mains 2021 Medium
- The function \(\mathrm{f}(\mathrm{x})\), that satisfies the condition \(\mathrm{f}(\mathrm{x})=\mathrm{x}+\int_{0}^{\pi / 2} \sin \mathrm{x} \cdot \cos y \mathrm{f}(\mathrm{y}) \mathrm{dy}\), is :JEE Mains 2021 Hard
- If \(f\left( x \right) = \left[ x \right] - \left[ {\frac{x}{4}} \right],\,x \in R\) , where \([x]\) denotes the greatest integer function, thenJEE Mains 2019 Hard
- If the function \(f\) defined as \(f(x)\, = \frac{1}{x} - \frac{{k - 1}}{{{e^{2x}} - 1}}\) ,\(x\, \ne \,0,\) is continuous at \(x = 0.\) then the ordered pair \((k,f(0))\) is equal to?JEE Mains 2018 Hard
- Let \(f :R \to R\) be defined by \(f(x)\,\, = \,\,\frac{x}{{1 + {x^2}}},\,x\, \in \,R.\) Then the range of \(f\) isJEE Mains 2019 Hard
- Let \(\mathrm{A}=\{1,2,3,4\}\) and \(\mathrm{R}=\{(1,2),(2,3),(1,4)\}\) be a relation on \(\mathrm{A}\). Let \(\mathrm{S}\) be the equivalence relation on \(A\) such that \(\mathrm{R} \subset \mathrm{S}\) and the number of elements in \(\mathrm{S}\) is \(\mathrm{n}\). Then, the minimum value of \(\mathrm{n}\) is ...........JEE Mains 2024 Easy