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I just want to know if what i did is correct...please help Thank YOU!!!

∑(n =200

therefore the 2 condtions need to be satisfied for it to be Convergent.

i) is true

ii) lim b_n = 0 ?

L= lim (n--> ∞) (1-1/n)^n

= lim ( n--> 0^+) ln (1-t) / t = -1

= lim(n-->0^+) ln (-1/1/t) / (1) = -1

Thus, L=e^-1 = 1/e which not equal to O.

Therefore the series is not absolutely convergent and is divergent

AM I CORRECT????

∑(n =200

*to ∞) ( -1)^n (1-1/n)^n = (-1 + 1/n)*

This is a alternation SeriesThis is a alternation Series

therefore the 2 condtions need to be satisfied for it to be Convergent.

i) is true

ii) lim b_n = 0 ?

L= lim (n--> ∞) (1-1/n)^n

= lim ( n--> 0^+) ln (1-t) / t = -1

= lim(n-->0^+) ln (-1/1/t) / (1) = -1

Thus, L=e^-1 = 1/e which not equal to O.

Therefore the series is not absolutely convergent and is divergent

AM I CORRECT????

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