Home
Class 12
MATHS
The sum of the series 1+1/4.2!1/16.4!+1/...

The sum of the series `1+1/4.2!1/16.4!+1/64.6!+………to oo` is (A) `(e+1)/2sqrt(e)` (B) `(e-1)/sqrt(e)` (C) `(e-1)/+2sqrt(e)` (D) `(e-1)/sqrt(e)`

A

`(e-1)/(sqrte)`

B

`(e+1)/sqrte`

C

`(e-1)/(2sqrte)`

D

`(e+1)/(2sqrt(e))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

The sum of the series 1+1/4.2!1/16.4!+1/64.6!+………to oo is (A) (e+1)/(2sqrt(e)) (B) (e-1)/sqrt(e) (C) (e-1)/(2sqrt(e)) (D) (e+1)/2sqrt(e)

The sum of series 1/2!+1/4!+16!+………. is (A) (e^2-1)/2 (B) (e^2-2)/e (C) (e^2-1)/(2e) (D) )(e-1)^2)/(2e)

The sum of the series 1/(2!)-1/(3!)+1/(4!)-... upto infinity is (1) e^(-2) (2) e^(-1) (3) e^(-1//2) (4) e^(1//2)

If xlog_e(log_ex)-x^2+y^2=4 then ((dy)/(dx))_(atx=e) is equal to (A) (2e+1)/ sqrt(4+e^2) (B) e/(2sqrt(4+e^2)) (C) (2e+1)/(2(4+e^2)) (D) (2e-1)/(2sqrt(4+e^2))

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

A variable point P on the ellipse of eccentricity e is joined to the foci S and S' . The eccentricity of the locus of incentre of the triangle PSS' is (A) sqrt((2e)/(1+e)) (B) sqrt(e/(1+e)) (C) sqrt((1-e)/(1+e)) (D) e/(2(1+e))

Prove that (tan^(-1)(1/e))^(2)+(2e)/(sqrt(e^(2)+1) lt (tan^(-1) e)^2 + (2)/(sqrt(e^(2)+1)

The sum of the series ""(1^2)/(2!)+(2^2)/(3!)+(3^2)/(4!)+"i s" e+1 b. e-1 c. 2e+1 d. 2e-1

If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n tan A is equal 1//sqrt(2) (b) 1/2 (c) 1/2sqrt(2) (d) -1/(sqrt(2))