Question
The sum of the infinite series 1 + 3x + 4x2 + 10x3 + 18x4 + ... at x = 1/3 is
Answer: Option E
:
E
Option (e) S =1 + 3x + 4x2 + 10x3 + 18x4 +... ---------- (1)2x * S= 2x + 6x2 + 8x3 + 20x4 +..... ----------- (2) --- multiplying by 2xSubtracting (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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:
E
Option (e) S =1 + 3x + 4x2 + 10x3 + 18x4 +... ---------- (1)2x * S= 2x + 6x2 + 8x3 + 20x4 +..... ----------- (2) --- multiplying by 2xSubtracting (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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