I have a sequence x n = ( 2 n 3 + n n 3 + 3 i n n + 1 ) .

Question

I have a sequence      x    n    =      (                  2                  n          3                +        n                    n        3              +                  3        i        n                    n        +        1              )    .

rioolpijpgp · Accepted Answer

You can make life simpler if you avail yourself of the fact that a sequence of complex numbers converges to z iff its real part converges to

ℜ (z)

and its imaginary part converges to

ℑ (z)

This simplifies the algebra. For the real part, you have

| \frac{2 n^{3} + n}{n^{3}} - 2 | = \frac{1}{n^{2}} \to 0 a s n \to \infty .

For the imaginary part, you have

| \frac{3 n}{n + 1} - 3 | = \frac{3}{n + 1} \to 0 a s n \to \infty .

I have a sequence x n </msub> = ( 2 n

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