Could someone answer this question about Fractals and the Mandelbrot set?
I wonder whether I am wrong or the textbook is wrong in the following question: c = 1i/2
After it is counted with the formula c²+c and so on . . .
It gets -1/4 +1i/2, -3/16+1i/4, -7/256+13i/32
I think it should not be in the Mandelbrot set because it's growing(unbounded), but the textbook says it is in the Mandelbrot set and bounded. Could someone on earth prove the textbook to be right? I will much appreciate it. Anyway, the author is Prof. Bruce H. Edwards - University of Florida.

Question

Could someone answer this question about Fractals and the Mandelbrot set? 
I wonder whether I am wrong or the textbook is wrong in the following question: c = 1i/2
After it is counted with the formula c²+c and so on . . . 
It gets -1/4 +1i/2, -3/16+1i/4, -7/256+13i/32
I think it should not be in the Mandelbrot set because it's growing(unbounded), but the textbook says it is in the Mandelbrot set and bounded. Could someone on earth prove the textbook to be right? I will much appreciate it. Anyway, the author is Prof. Bruce H. Edwards - University of Florida.

phi · Answer

the magnitude of each term in the series approaches zero.  What makes you think it's growing?

anonymous · Answer

Oh, you are right. It makes sense to me now. I was somehow confused, and I thought the numbers were not back to the previous c = 1i/2 (meant growing) without noticing the quotients of those get close to zero. Well, I have just started Precalculus, so I need a lot of studies. Thanks to you and this site. You are real π. It helps! :)