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If 1+2x +3x^2+4x^3 +…..oo ge 4 then...

If `1+2x +3x^2+4x^3 +…..oo ge 4 ` then

A

least value of x is 1/2

B

greatest value of x is 4/3

C

least value of x is 2/3

D

greatest value of x does not exist

Text Solution

Verified by Experts

The correct Answer is:
A, D
`S=1+2x+3x^(2)+4x^(3)+….oo`
`rArrxS=x+2x^(2)+3x^(3)+4x^(4)+..oo`
`rArr(1-x)S=1+x+x^(2)+…oo=1/(1-x)`
`rArrS=1/((1-x)^(2))`
Now, `Sge4`
`rArr1/((1-x)^(2))gt4`
`rArr(x-1)^(2)le1/4`
`rArr-1/2lex-1le1/2`
`rArr1/2lexle3/2`. Also `0ltabsxlt1`
`rArr1/2lexlt1`
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