A Let y = 0.1234567891011121314151617181920..., whose digits are the natural numbers in decimal form, strung end...

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A Let y = 0.1234567891011121314151617181920..., whose digits are the natural numbers in decimal form, strung end to end. Prove that y is irrational. Is 0-101001000100001..., where each successive string of Os has one more digit, rational or irrational? 8 Say whether each of the following sequences (an) tends to a limit, and if so, what the limit is. Use the & N definition to prove your answers are correct. (a) an = n² (b) an = 1/(n² + 1) (c) an = 1 ++ (d) an = (-1)" (e) an = (-)" + (-)" A Let y = 0.1234567891011121314151617181920..., whose digits are the natural numbers in decimal form, strung end to end. Prove that y is irrational. Is 0-101001000100001..., where each successive string of Os has one more digit, rational or irrational? 8 Say whether each of the following sequences (an) tends to a limit, and if so, what the limit is. Use the & N definition to prove your answers are correct. (a) an = n² (b) an = 1/(n² + 1) (c) an = 1 ++ (d) an = (-1)" (e) an = (-)" + (-)"