The sum of the infinite series 1-3 x-4 x2-10 x3-18 x4- at x-1 - 3 is

The correct option is D none of theseOption (e) S =1 + 3x + 4x2 + 10x3 + 18x4 +... ——— (1)2x * S= 2x + 6x2 + 8x3 + 20x4 +..... ———– (2) — multiplying by 2x ...

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Quantitative Aptitude

A.M Greater than or Equal to G.M

The sum of th...

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The sum of the infinite series 1 + 3x + 4x² + 10x³ + 18x⁴ + ... at x = 1/3 is

28/9

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25/8

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49/16

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3/4

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none of these

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Solution

The correct option is E none of these
Option (e) S =1 + 3x + 4x² + 10x³ + 18x⁴ +... ---------- (1)
2x * S= 2x + 6x² + 8x³ + 20x⁴ +..... ----------- (2) --- multiplying by 2x
Subtracting (2) from (1), we get
= (1 - 2x)S= 1 + x - 2x²(1 - x + x² - x³ ......)
= (1 - 2x)S= 1 + x - 2x²/(1+x) [since 0<x <1 and sum of infinite series]
Now substituting x = 1/3 we get S = 7/2
Hence, choice (e) is the correct answer.

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The sum of the infinite series 1 + 3x + 4x2 + 10x3 + 18x4 + ... at x = 1/3 is

The sum of the infinite series 1 + 3x + 4x² + 10x³ + 18x⁴ + ... at x = 1/3 is