If x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1 Then x is equal to

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17 May 2010 Find the value of x

If x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
Then x is equal to

OPtion

1) 2/3
2) 1/3
3) 1/4
4) 1/2
5) 4/5
6) 8/9
7) 1/5
8) 3/5
9) 2/9
10) 7/8

Solution

x + x^2 + x^3 + x^4 + x^5 + x^6 +........ Upto ∞ = 1
x (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 +........ Upto ∞) = 1
x [1 + (x + x^2 + x^3 + x^4 + x^5 + x^6 +........ Upto ∞)] = 1
x [1 + 1] = 1
x = 1/2

Correct Option: 4 Best Solution (19)

Saswata Chakraborty   14 years AGO

x+x^2+x^3+x^4+......upto infinity=x/(1-x)=1(given)
solving x=1/2

Like? Yes (1) | No   

Dr.Dipin Singh   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
It is a GP series qith a=x and r=x, then sum of series = a/(1-r) = x/(1-x) - 1 or x= 1-x, then 2x=1, x=1/2

Like? Yes (1) | No   

Prashant Khare   14 years AGO

Its a Infinite Geometric Progression with first term as \'x\' and common ration as \'x\'. So Sum of GP
x/(1-x) = 1 which gives x = 1/2.

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Pargat Pal Singh   14 years AGO

Given x + x^2 + x^3 + x^4 + x^5 + x^6 +..infinity = 1
sum of GP series = x/(1-x) - 1 or x= 1-x, or x=1/2

Like? Yes (1) | No   

HARMEET KAUR   14 years AGO

Here x + x^2 + x^3 + x^4 + x^5 +..infinity = 1
sum of GP series = x/(1-x) = 1 or x= 1-x,
.......................
Hence x=1/2

Like? Yes (1) | No   

Saranjit Singh   14 years AGO

If x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1

or
x/(1-x) =1
Then x is equal to 1/2 .... option 4

Like? Yes (1) | No   

Mayur   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞ = 1, then
x/1-x=1....... x=1/2

Like? Yes (1) | No   

Neha Bhatia   14 years AGO

x(1/(1-x))=1
x=1-x
x=1/2

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S. Singh   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +..infy = 1
sum of this GP series = x/(1-x) - 1 or x=1/2.. option 4

Like? Yes (1) | No   

SUDESHNA SEN   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
So, x(1+x^2+x^3+..... upto infinite)=1
or, x{1/(1-x)}=1
or, x/(1-x)=1
or, x=1-x
or, 2x=1
or, x=1/2....Option 4)

Like? Yes (1) | No   

Mamon Sengupta   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
So, x(1+x^2+x^3+..... upto infinite)=1
or, x{1/(1-x)}=1
or, x/(1-x)=1
or, x=1-x
or, 2x=1
or, x=1/2....Option 4)

Like? Yes (1) | No   

Trishita Dasgupta   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
So, x(1+x^2+x^3+..... upto infinite)=1
or, x{1/(1-x)}=1
or, x/(1-x)=1
or, x=1-x
or, 2x=1
or, x=1/2....Option 4)

Like? Yes (1) | No   

ASHOK ROY   14 years AGO

x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
So, x(1+x^2+x^3+..... upto infinite)=1
or, x{1/(1-x)}=1
or, x/(1-x)=1
or, x=1-x
or, 2x=1
or, x=1/2....Option 4)

Like? Yes (1) | No   

sanjib biswas   14 years AGO

this is GP series and its sum a/1-r i.e.
(1/2)/(1-1/2)=1 then answer is 1/2

Like? Yes (1) | No   

RASHI   14 years AGO

x/(x-1)=1
x=x-1
x=1/2

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Dimple   14 years AGO

If x + x^2 + x^3 + x^4 + x^5 + x^6 +.......... Upto ∞(infinite) = 1
or x/(1-x)=1 or x=1-x or 2x=1 or x=1/2

Like? Yes (1) | No   

sivakumar   14 years AGO

x+x^2+x^3+x^4+..... = x(1+x+x^2+x^3+....)=1; x(1+1)=1; x=1/2;

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Vasu   14 years AGO

Simple GP problem with a=1/2 and r=1/2 and sum =1

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Sukham   14 years AGO

Sum of reducing GP series up to infinity is equal to a/(1-r).
here a=x, r=x, then sum = x/(1-x)=1 means x=1/2

Like? Yes (1) | No