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This is a beautiful problem from ISI MStat 2018 problem 2, which uses the cute little ideas of telescopic sum and partial fractions.

Let be a sequence defined by and

Show that converges and find its limit.

- Telescopic Sum

.

.

.

This is a beautiful problem from ISI MStat 2018 problem 2, which uses the cute little ideas of telescopic sum and partial fractions.

Let be a sequence defined by and

Show that converges and find its limit.

- Telescopic Sum

.

.

.

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Thank you! Really helpful ?

please check if the ans is (7/4)^1/3 . I think there is minus missing in the 4th line .