Sigma(n=1)^(oo) (x^(2n))/(2n-1) is equa...

`Sigma_(n=1)^(oo) (x^(2n))/(2n-1)` is equal to

`(x)/(2)log_(e)((1+x)/(1+x))`

`1/2log_(e)((1+x^(2))/(1-x^(2)))`

`xlog_(e)((1+x)/(1-x))`

none of these

Text Solution

AI Generated Solution

To solve the series \( \Sigma_{n=1}^{\infty} \frac{x^{2n}}{2n-1} \), we can follow these steps: ### Step 1: Rewrite the Series We start with the series: \[ S = \sum_{n=1}^{\infty} \frac{x^{2n}}{2n-1} \] This can be rewritten as: ...

Topper's Solved these Questions

EXPONENTIAL AND LOGARITHMIC SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos
EXPONENTIAL AND LOGARITHMIC SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|37 Videos
EXPONENTIAL AND LOGARITHMIC SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos
ELLIPSE
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos
HEIGHTS AND DISTANCES
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

Similar Questions

Explore conceptually related problems

sum_(n=1)^(oo) (1)/(2n(2n+1)) is equal to

The vlaue of the Sigma_(n=0)^(oo) (2n+3)/(3^n) is equal to ______.

The sum of series Sigma_(n=1)^(oo) (2n)/(2n+1)! is

If a = Sigma_(n=1)^(oo) (2n)/(2n-1!),b=Sigma__(n=1)^(oo) (2n)/(2n+1!) then ab equals

Let a=Sigma_(n=0)^(oo) (x^(3n))/((3n))!, b =Sigma_(n=1)^(oo) (x^(3n-2))/(3n-2)! and C=Sigma_(n=1)^(oo) (x^(3n-1))/(3n-1)! and w be a complex cube root of unity Statement 1: a+b+c =e^(x),a+bw+cw^(2)=e^(wx) and a+bw^(2)+cw=e^(w^(2)) Statement 2: a^(3)+b^(3)+C^(3)-3abc=1

If a=Sigma_(n=0)^(oo) (x^(3x))/(3n)!,b=Sigma_(n=1)^(oo)(x^(3n-2))/(3n-2!) and C= Sigma_(n=1)^(oo)(x^(3n-1))/(3n-1!) then the value of a^(3)+b^(3)+C^(3)-3abc is

sum_(n=1)^(oo) (2n)/(n!)=

If S=Sigma_(n=0)^(oo) (logx)^(2n)/(2n!) , then S equals

The sum sum_(n=1)^oo tan^(-1)(3/(n^2+n-1)) is equal to

sum_(n=1) ^(oo) (1)/((2n-1)!)=

OBJECTIVE RD SHARMA ENGLISH-EXPONENTIAL AND LOGARITHMIC SERIES-Section I - Solved Mcqs

In the expansion of log(10)(1-x),|x|lt1 the coefficient of x^(n) is
Text Solution
|
Sum of series 9/(1!)+19/(2!)+35/(3!)+57/(4!)+... (A) 7e-3 (B) 12e-5...
Text Solution
|
The constant term in the expansion of (3^(x)-2^(x))/(x^(2)) is
Text Solution
|
Sigma(n=1)^(oo) (x^(2n))/(2n-1) is equal to
Text Solution
|
Then sum of the series 1+(1+3)/(2!)x+(1+3+5)/(3!)x^(2)+(1+3+5+7)/(4...
Text Solution
|
1/(e^(3x))(e^x+e^(5x))=a0+a1x+a2x^2+........=>2a1+2^3a3+2^5a5+......=
Text Solution
|
Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C=1-(x^(2))/(2!)+(x^(4))/(4!) T...
Text Solution
|
The sum of series 2/(3!)+4/(5!)+6/(7!)+...........oo is :
Text Solution
|
The sum of the series S=Sigma(n=1)^(infty)(1)/(n-1)! is
Text Solution
|
The sum of the series loge(3)+(loge(3))^3/(3!)+(loge(3))^5/(5!)+....+ ...
Text Solution
|
The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...
Text Solution
|
(1+3)loge3+(1+3^2)/(2!)(loge3)^2+(1+3^3)/(3!)(loge 3)^3+....oo= (a)28...
Text Solution
|
If agt0 and x in R, then 1+(xlog(e)a)+(x^(2))/(2!)(log(e)a)^(2)+(x^(...
Text Solution
|
(2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+….infty is equal to
Text Solution
|
1+(2x)/(1!)+(3x^(2))/(2!)+(4x^(3))/(3!)+..infty is equal to
Text Solution
|
1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2)))+1/6((1)/(2^(3))+(1)/(3^(3)))...
Text Solution
|
The sum of series (1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3...
Text Solution
|
The sum of the series (1)/(2!)+(1)/(4!)+(1)/(6!)+..to infty is
Text Solution
|
If 0ltylt2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)/(5x...
Text Solution
|
The sum of the series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+..to infty is...
Text Solution
|