1 2 Use the argument to show that 1 1 n n e as n (Hint First prove the inequality x x2 2 log(1 x) x, x 0 ) ...

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1.2 Use the - argument to show that 1 + 1 n n e...

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1.2 Use the -δ argument to show that

1 + 1 n

−→ e as n → ∞. (Hint: First prove the inequality x − x2/2 ≤ log(1 + x) ≤ x, x > 0.)

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