Note the following sequence:
The question is, for which complex z values does it converge for n->infinity, giving limits, and for which complex z values does it diverge to infinity in C?
For which complex values of z (if any) do the following sequences converge as n → ∞ (give the limits when they do) and for which complex values of z (if any) do they diverge to ∞ in C?
Heres the sequence
an(z)=(1+(z/n))^n
Given Sequence :
So
(its formula)
(z=a+ib, a, b are real)
so for unique value for b=0, i. e. imaginary part must be zero.
So,
i. e. limit exist.
Hence, for limit to be exist z must be real i. e. z belongs to set of real numbers. And it diverges or diverges to infinity when z is not real.
Note the following sequence: The question is, for which complex z values does it converge for...
Question 4. (a) Let c be a cluster point of a set S. Prove directly from the e, o definition of continuity that the complex valued function f() is continuous within S at the point c if and only if both of the functions Re[f(a) and Im[f(2)] are continuous within S at the point c (b) For which complex values of (if any) do the following sequences converge as n → oo (give the limits when they do) and for...
help.PNGa. Find a formula for the general term .
b. Does this sequence converge or diverge? Why?
c. Does the series converge or diverge? Why?I did part (a) already since it was the easiest one and I got a_n=3/(4n). correct me if I am wrong. However, I do not know which test to use for part b and c.
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