English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative:The value of 1-12(23)+13(23)2 14(23)3+... is - Mathematics

Advertisements
Advertisements

Question

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

Options

  • `log (5/3)`

  • `3/2 log (5/3)`

  • `5/3 log (5/3)`

  • `2/3 log (2/3)`

MCQ

Solution

`3/2 log (5/2)`

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 20 | 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

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


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

`(x + 2) - 2/3`


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


Prove that `sqrt((1 - x)/(1 + x))` is approximately euqal to `1 - x + x^2/2` when x is very small


Write the first 6 terms of the exponential series
e5x 


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


Write the first 4 terms of the logarithmic series
log(1 + 4x) 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) + ...`


If p − q is small compared to either p or q, then show `root("n")("p"/"q")` `(("n" + 1)"p" + ("n" - 1)"q")/(("n"- 1)"p" +("n" + 1)"q")`. Hence find `root(8)(15/16)`


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


Choose the correct alternative:
If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn − 2Sn−1 + Sn−2 is


Choose the correct alternative:
The value of the series `1/2 + 7/4 + 13/8 + 19/16 + ...` 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 value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×