English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative:The value of 12!+14!+16!+... is

Advertisements
Advertisements

Question

Choose the correct alternative:
The value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is

Options

  • `("e"^2 + 1)/(2"e")`

  • `("e" + 1)^2/(2"e")`

  • `("e" - 1)^2/(2"e")`

  • `("e"^2 - 1)/(2"e")`

MCQ
Advertisements

Solution

`("e" - 1)^2/(2"e")`

shaalaa.com
Infinite Sequences and Series
  Is there an error in this question or solution?
Chapter 5: Binomial Theorem, Sequences and Series - Exercise 5.5 [Page 233]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 5 Binomial Theorem, Sequences and Series
Exercise 5.5 | Q 19 | Page 233

RELATED QUESTIONS

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`1/(5 + x)`


Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`2/(3 + 4x)^2`


Find `root(3)(10001)` approximately (two decimal places


Prove that `root(3)(x^3 + 6) - root(3)(x^3 + 3)` is approximately equal to `1/x^2` when x is sufficiently large


Write the first 6 terms of the exponential series
e5x 


Write the first 6 terms of the exponential series
`"e"^(-2x)`


Write the first 6 terms of the exponential series
`"e"^(1/2x)`


Write the first 4 terms of the logarithmic series
log(1 – 2x) Find the intervals on which the expansions are valid.


Write the first 4 terms of the logarithmic series
`log((1 + 3x)/(1 -3x))` Find the intervals on which the expansions are valid.


Write the first 4 terms of the logarithmic series
`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.


If y = `x + x^2/2 + x^3/3 + x^4/4  ...`, then show that x = `y - y^2/(2!) + y^3/(3!) - y^4/(4) + ...`


Find the coefficient of x4 in the expansion `(3 - 4x + x^2)/"e"^(2x)`


Choose the correct alternative:
The coefficient of x6 in (2 + 2x)10 is


Choose the correct alternative:
The coefficient of x8y12 in the expansion of (2x + 3y)20 is


Choose the correct alternative:
The sum up to n terms of the series `1/(sqrt(1)  +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ...` is 


Choose the correct alternative:
The sum of an infinite GP is 18. If the first term is 6, the common ratio is


Choose the correct alternative:
The coefficient of x5 in the series e-2x is


Choose the correct alternative:
The value of `1 - 1/2(2/3) + 1/3(2/3)^2  1/4(2/3)^3 + ...` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×