Limit(n->oo) {(1+x) (1+x^2)(1+x^4).........

`Limit_(n->oo) {(1+x) (1+x^2)(1+x^4).......(1+x^(2^n))}=` if `|x|<1` has the value equal to

A

0

B

1

C

1-x

D

`(1-x)^(-1)`

Text Solution

Verified by Experts

The correct Answer is:

D

Topper's Solved these Questions

LIMIT
MOTION|Exercise EXERCISE -2( LEVEL-I)|16 Videos
LIMIT
MOTION|Exercise EXERCISE-2(LEVEL-2)|5 Videos
LIMIT
MOTION|Exercise EXERCISE-4|17 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
MOTION|Exercise Exercise -4 Level -II|7 Videos
MATRICES
MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

Similar Questions

Explore conceptually related problems

Lim it_(n rarr oo){(1+x)(1+x^(2))(1+x^(4))......(1+x^(2^(n)))}= if |x|<1 has the value equal to

if |x|<1 then (Lt)_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))......*(1+x^(2n))=

If |x|<1 , then lim_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))...(1+x^(2^n))=

f(x)=lim_(n rarr oo)(1+x)(1+x^(2))(1+x^(4))..........(1+x^(2^(n-1))) then

Prove by mathematical induction that (1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+.....+(2^n)/(1+x^(2^n))=(1)/(x-1)+(2^(n+1))/(1-x^(2^(n+1))) where , |x|ne 1 and n is non - negative integer.

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a)-1 (b). 1 ( c.) 0 (d).2

Find the value of (1+x)^(n)+nc_(1)(1+x)^(n-1)*(1-x)+^(n)C_(2)(1+x)^(n-2)(1-x)^(2)+.........+(1-x)^(n)

n + (n-1) x + (n-2) x ^ (2) + ....... + 2x ^ (n-2) + x ^ (n-1)

MOTION-LIMIT-EXERCISE -1

underset( n rarr oo) ( "Lim") ( -3n + (-1)^(n))/(4n-(-1)^(n)) is
Text Solution
|
lim(xto oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greate...
Text Solution
|
Limit(n->oo) {(1+x) (1+x^2)(1+x^4).......(1+x^(2^n))}= if |x|<1 has th...
Text Solution
|
The graph of the function f(x) = underset( t rarr 0 ) ("Lim") ((2x)/(p...
Text Solution
|
Let f(x)=(loge(x^2+e^x))/(loge(x^4+e^2x)). If lim(xto oo) f(x)=l and l...
Text Solution
|
If [x] denotes the greatest integer le x , then underset( n rarr oo ) ...
Text Solution
|
lim(n->oo) 1/sqrt(n^2)+1/sqrt(n^2+1)+1/sqrt(n^2+2)+.....1/sqrt(n^2+2n)...
Text Solution
|
The limit underset( theta rarr0 ) ("lim") ([ (nsin theta)/( theta) ]+ ...
Text Solution
|
lim(x->-oo) {x^2*sin(1/x)}/sqrt(9x^2+x+1) is equal to
Text Solution
|
lim(x->oo)(x^2sin(1/x)+x+1)/(x^2+x+1) is equal to
Text Solution
|
Evaluate: ("lim")(nvecoo)ncos(pi/(4n))sin(pi/(4n)) where (x , y)vec(0...
Text Solution
|
lim(x->pi/2) ((1-tan(x/2))(1-sinx))/((1+tan(x/2))((pi-2x)^3))
Text Solution
|
The limit underset( x rarr0 ) ( "lim") ( 1- cos x sqrt( cos 2x))/( x^(...
Text Solution
|
lim(x->0^+)cos^(- 1)(1-x)/(sqrt(x))
Text Solution
|
underset( x rarr 0 ) ("lim") [ ( 1-e^(x)) ( sin x )/( |x|)] is equal ...
Text Solution
|
Evaluate: underset(hrarr0)("lim")(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(...
Text Solution
|
lim(x->0) sin(6x^2)/(lncos(2x^2-x)
Text Solution
|
The value of underset( x rarr 0 ) ( "Lim") ( sin ( ln ( 1+ x)))/( ln (...
Text Solution
|
underset( x rarr pi //2) ("Lim") ( 2 ^(cos x) - 1)/( x ( x-pi //2))= ...
Text Solution
|
lim(x->0)((4^x-1)^3)/(sin(x/p)ln(1+(x^2)/3) is equal to
Text Solution
|