The sum $\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}$ is equal to :

  • [JEE MAIN 2023]
  • A

    $\frac{11 e }{2}+\frac{7}{2 e }$

  • B

    $\frac{13 e }{4}+\frac{5}{4 e }-4$

  • C

    $\frac{11 e }{2}+\frac{7}{2 e }-4$

  • D

    $\frac{13 e }{4}+\frac{5}{4 e }$

Similar Questions

If $x, y, z \in R^+$ are such that $z > y > x > 1$ , ${\log _y}x + {\log _x}y = \frac{5}{2}$ and ${\log _z}y + {\log _y}z = \frac{{10}}{3}$ then ${\log _x}z$ is equal to

Solution set of equation

$\left| {1 - {{\log }_{\frac{1}{6}}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 - {{\log }_{\frac{1}{6}}}x + {{\log }_{\frac{1}{2}}}x} \right|$ is $\left[ {\frac{a}{b},a} \right],a,b, \in N,$ then the value of $(a + b)$ is

The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is

If ${\log _{10}}x + {\log _{10}}\,y = 2$ then the smallest possible value of $(x + y)$ is

If ${x^{{3 \over 4}{{({{\log }_3}x)}^2} + {{\log }_3}x - {5 \over 4}}} = \sqrt 3 $ then $x$ has