Question:
If
f(x)=(x)/(1+x)+(x)/((x+1)(2x+1))+(x)/((2x+1)(3x+1))+⋯
then at x=0, f(x)
If
f(x)=(x)/(1+x)+(x)/((x+1)(2x+1))+(x)/((2x+1)(3x+1))+⋯
then at x=0, f(x)
Show Hint
Telescoping series often lead to smooth, differentiable functions.
Updated On: Mar 20, 2026
- has no limit
- is not continuous
- is continuous but not differentiable
- is differentiable
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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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