Need help with limit, urgent!!!?

Question

I really gave no idea how to do these questions, I have been pondering about these for a couple days. But still don't get it. Help please

1) lim n--->∞ 1 + (-1)^n <<< for this question that (-1)^n is oscillate isn't it, I'm not sure what to do next

2) lim n--->∞ (1/2)^n + (-2)^n

3) lim n--->∞ (5^n + 4^n)/9^n-2^n

4) lim n--->∞ (4^n+1 + 3^n)/(4^n - (-3)^n+1)

5) lim n--->∞ (3^n - 2^n)

4) lim n--->∞ [(-3)^n]/(2^n - 1) <<< two to the power n, minus one

Thanks in advance you help me a lot.

ไม่ประสงค์ออกนาม · Accepted Answer

1. This has no limit because it continually oscillates between 0 and 2 and therefore does not approach a single fixed number.

2. The (1/2)^n will gradually approach 0 but what happens to (-2)^n ? Again no limit.

3. Is this (5^n + 4^n) / (9^n - 2^n) ?
If so then consider that when n gets very large the 9^n will be so much larger than the others that the denominator will predominate.

4. Again consider that when n is very large the power of 4 will be very much larger than the power of 3. So much so that the 3^n on top will make little difference to the 4^n+1 and the 3^n+1 on bottom will make little impact on the 4^n. 

5, 6. You should have the idea by now.

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