If and , then which of the following is true? (Notation: denotes the modulus of and is the factorial of .)
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4 marks, −1MathematicsSequences, series and convergenceArithmetic and geometric progressions and special seriesHardabout 3 min
DSE 2021 Question 7: Sequences, series and convergence
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If |x| < 1 and y = Σₖ₌₁^∞ (-1)^(k+1) x^k/k, then which of the following is true? (Notation: |x| denotes the modulus of x and k! is the factorial of k .) (A) x = Σₖ₌₁^∞ (-1)^k y^k/k (B) x = Σₖ₌₁^∞ k/y^k (C) x = Σₖ₌₁^∞ y^k/k! (D) x = Σₖ₌₁^∞ (-1)^k y^k/k!
Also written as: If |x| < 1 and y = sum_(k=1)^(inf) (-1)^(k+1) x^k/k, then which of the following is true? (Notation: |x| denotes the modulus of x and k! is the factorial of k .)
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What this question tests
This question is on Arithmetic and geometric progressions and special series, part of Sequences, series and convergence in Mathematics.
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