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Question: Sum of infinite series 1 – 3x + 5x<sup>2</sup> – 7x<sup>3</sup> … ¥ is 2, (\| x \| \< 1) then x =...

Sum of infinite series 1 – 3x + 5x2 – 7x3 … ¥ is 2, (| x | < 1) then x =

A

14(−5±17)\frac { 1 } { 4 } ( - 5 \pm \sqrt { 17 } )

B

−14(5+17)- \frac { 1 } { 4 } ( 5 + \sqrt { 17 } )

C

17−54\frac { \sqrt { 17 } - 5 } { 4 }

D

None

Answer

17−54\frac { \sqrt { 17 } - 5 } { 4 }

Explanation

Solution

S¥ = ̃ 2 =

̃ 2 + 4x + 2x2 = 1 – x

̃ 2x2 + 5x + 1 = 0

̃ x = −5±174\frac { - 5 \pm \sqrt { 17 } } { 4 }

But | x | < 1

̃ x = −5+174\frac { - 5 + \sqrt { 17 } } { 4 }