1. Sequence Limits

Sequence Limits

Calculate the limit of the sequences

1) \(u_n = \frac{n}{n+1}\)

2) \(u_n = \frac{4n-3}{6-5n}\)

3) \(u_n = \frac{n^2-1}{3-n^3}\)

4) \(u_n = \frac{2n^3-4n-1}{6n+3n^2-n^3}\)

5) \(u_n = \frac{(n-1)(n+3)}{3n^2+5}\)

6) \(u_n = \frac{(2n-1)^2}{(4n-1)(3n+2)}\)

7) \(u_n = \frac{(2n-1)^3}{(4n-1)^2(1-5n)}\)

8) \(u_n = \frac{3}{n} - \frac{10}{\sqrt{n}}\)

9) \(u_n = \frac{(-1)^n}{2n-1}\)

10) \(u_n = (\frac{2n-3}{3n+1})^2\)

11) \(u_n = (\frac{5n-2}{3n-1})^3\)

12) \(u_n = \frac{(\sqrt{n}+3)^2}{n+1}\)

13) \(u_n = \frac{\sqrt{n}-2}{3n+5}\)

14) \(u_n = \frac{n-10}{3}\)

15) \(u_n = \frac{(-0,8)^n}{2n-5}\)

16) \(u_n = \frac{2-5n-10n^2}{3n+15}\)

17) \(u_n = \frac{2n+(-1)^n}{n}\)

18) \(u_n = \frac{\sqrt{1+2n^2}-\sqrt{1+4n^2}}{n}\)

19) \(u_n = \sqrt{\frac{3n-2}{n+10}}\)

20) \(u_n = \sqrt[3]{\frac{n-1}{8n+10}}\)

21) \(u_n = \frac{\sqrt{n^2+4}}{3n-2}\)

22) \(u_n = \frac{n}{\sqrt[3]{n^3+1}}\)

23) \(u_n = \frac{n}{\sqrt[3]{8n^3-n}-n}\)

24) \(u_n = \frac{1}{\sqrt{4n^2+7n}-2n}\)

25) \(u_n = \sqrt{n+2}-\sqrt{n}\)

26) \(u_n = \sqrt{n^2+n}-n\)

27) \(u_n = n-\sqrt{n^2+5n}\)

28) \(u_n = \sqrt{3n^2+2n-5}-n\sqrt{3}\)

29) \(u_n = 3n-\sqrt{9n^2+6n-15}\)

30) \(u_n = \sqrt[3]{n^3+4n^2}-n\)

31) \(u_n = \sqrt[3]{n^2(2-\sqrt[3]{2n^3+5n^2-7})}\)

32) \(u_n = \frac{4^{n}-1}{2^{2n}-7}\)

33) \(u_n = \frac{5 \cdot 3^{2n}-1}{4 \cdot 9^n+7}\)

34) \(u_n = \frac{3 \cdot 2^{2n+2}-10}{5 \cdot 4^{n-1}+3}\)

35) \(u_n = \frac{-8^n-1}{7^{n+1}}\)

36) \(u_n = \frac{2^{n+1}-3^{n+2}}{3^{n+2}}\)

37) \(u_n = (\frac{3}{2})^{n} \frac{2^{n+1}-1}{3^{n+1}-1}\)

38) \(u_n = \sqrt[n]{3^n+2^n}\)

39) \(u_n = \sqrt[n]{10^n+9^n+8^n}\)

40) \(u_n = \sqrt[n]{10^{100}-\frac{1}{10^{100}}}\)

41) \(u_n = \sqrt[n]{(\frac{2}{3})^n+(\frac{3}{4})^n}\)

42) \(u_n = \frac{1+2+...+n}{n^2}\)

43) \(u_n = \frac{1^2+2^2+...+n^2}{n^3}\)