The sum of series (1)^(2)/(1.2!)+(1^(2...

The sum of series
`(1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3^(2))//(3.4!)+..+(1^(2)+2^(2)+…+n^(2))/(n.(n+1))!+..infty` is equals to

A

`e^(2)`

B

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

C

`(3e-1)/(6)`

D

40

Text Solution

Verified by Experts

Required sum
`=underset(n=1)overset(infty)Sigma(1^(2)+2)^(2)+..+(n^(2))/(n.(n+1))!`
`=underset(n=1)overset(infty)Sigman((n+1)(2n+1))/(6n(n+1))!=1/6 underset(n=1)overset(infty)Sigma (1)/(n-1)!+underset(1)/(n!)}`
`=16(2e+e-1)=(3e-1)/(6)`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

EXPONENTIAL AND LOGARITHMIC SERIES
OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|5 Videos
EXPONENTIAL AND LOGARITHMIC SERIES
OBJECTIVE RD SHARMA|Exercise Exercise|37 Videos
EXPONENTIAL AND LOGARITHMIC SERIES
OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos
ELLIPSE
OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos
HEIGHTS AND DISTANCES
OBJECTIVE RD SHARMA|Exercise Exercise|45 Videos

Similar Questions

Explore conceptually related problems

The sum of the series 1+(1+2)/(2!)+(1+2+2^(2))/(3!)+(1+2+2^(2)+2^(3))/(4!)+ is equal to

The sum of the series (1^(2))/(1!)+(2^(2))/(2!)+(3^(2))/(3!) +……to infty is

The sum to n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(2))+--

The sum of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(2))+...... upto n terms,is

Find the sum to n terms of the series 1^(2)/(1)+(1^(2)+2^(2))/(1+2)+(1^(2)+2^(2)+3^(2))/(1+2+3)+cdots

The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2)-3^(2))+ . . . . , is

Find the sum of the series (1^(2)+1)1!+(2^(2)+1)2!+(3^(2)+1)3!+ . .+(n^(2)+1)n! .

The sum of the series 1^(2)+1+2^(2)+2+3^(2)+3+ . . . . .. +n^(2)+n , is

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2))/(1^(3))+(2^(2))/(2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

The sum of the series (1^(2)+1)*1!+(2^(2)+1)*2!+(3^(2)+1).3!+......+(n+1)*n!

OBJECTIVE RD SHARMA-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))+…in...
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
|