Question

For 0 < x < 1, the value of log(1 + x) + log(1 + x²) + .... to ∞ is

• A. log(1− x)
• B. − log(1 − x)
• C. logx
• D. −logx

Answer 1

Answer: (B)

− log(1 − x)

Answer 2

The given expression = log [(1 + x) (1 + x²) ..... to ∞]

= log[ 1+ x + x² + x³ + .... to ∞]

= log$\left( \frac{1}{1 - x} \right)$

= − log(1 − x).