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This problem is a simple application of the sequential definition of continuity from ISI MStat 2015 PSB Problem 1 based on Telescopic Continuity.

Let be a function which is continuous at 0 and

Also assume that satisfies the following relation for all :

Find .

Add them all up. That's the telescopic elegance.

Observe that since, is continuous at .

Hence take limit on , and we get .

- Find the general function from the given condition.
- What if is not continuous?

This problem is a simple application of the sequential definition of continuity from ISI MStat 2015 PSB Problem 1 based on Telescopic Continuity.

Let be a function which is continuous at 0 and

Also assume that satisfies the following relation for all :

Find .

Add them all up. That's the telescopic elegance.

Observe that since, is continuous at .

Hence take limit on , and we get .

- Find the general function from the given condition.
- What if is not continuous?

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