Question:
If
\[
f(x) = \frac{x}{1+x} + \frac{x}{(x+1)(2x+1)} + \frac{x}{(2x+1)(3x+1)} + \cdots
\]
then at \(x = 0\), \(f(x)\) is:
If
\[ f(x) = \frac{x}{1+x} + \frac{x}{(x+1)(2x+1)} + \frac{x}{(2x+1)(3x+1)} + \cdots \]
then at \(x = 0\), \(f(x)\) is:
\[ f(x) = \frac{x}{1+x} + \frac{x}{(x+1)(2x+1)} + \frac{x}{(2x+1)(3x+1)} + \cdots \]
then at \(x = 0\), \(f(x)\) is:
Show Hint
Telescoping series often lead to smooth, differentiable functions.
Updated On: Mar 23, 2026
- has no limit
- is not continuous
- is continuous but not differentiable
- is differentiable
Show Solution
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The Correct Option is D
Solution and Explanation
The series telescopes and converges smoothly at x=0, hence the function is differentiable at x=0.
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