## Description

Problem 6 (Exercise 2.14). Give an example of an open cover of the segment (0*,* 1) which has no finite subcover.

Problem 7 (Exercise 2.18). Is there a nonempty perfect set in R^{1} which contains no rational number?

Problem 8 (Exercise 2.20). Are closures and interiors of connected sets always connected?

√

Problem 9 (Exercise 3.3). If *s*_{1} = 2, and

*s*_{n}_{+1}* *= 2 + ^{√}*s*_{n} (*n* = 1*,* 2*,* 3*, . . .* )*,*

prove that *{s*_{n}*}* converges, and that *s*_{n} *<* 2 for *n* = 1*,* 2*,* 3*, . . .* .

Problem 10 (Exercise 3.7). Prove that the convergence of *a*_{n}* *implies the convergence of

^{√}_{a}_{n}* **n*

if *a*_{n} *≥* 0.

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