More importantly are approach and equal the same as when we evaluate any limit we in end say that limit IS EQUAL TO some value , or there is no limit, but how can something APPROACHING is EQUAL TO SOMETHING . When we evaluate limit as x approaches zero , it is very similar to f(0), so why do we need limit st all.
Actually if we do NOT say then it is equal to it then we cannot find the limit. And other things is that limit itself means that it is NOT the exact value of the function BUT is the value approaching from either side.
limit itself means that it is NOT the exact value of the function BUT is the value approaching from either side, I learned this when I did custom essay help a few days back
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But 1/2 + 1/4 +1/8 + 1/16 + . . . actually does equal exactly 1
Have you ever seen anyone actually write 1/2 + 1/4 +1/8 + 1/16 + . . . = approx. 1 ?
It's the same for .99999 repeat. It is actually equal to 1. Are really trying to say that .999... is not = 1? I hope not because if you are then you are wrong. They represent the same point on the real number line and by default they are equal.
Now in order to reach equality you actually have to add up all of the infinite number of terms. This is not difficult and for some reason this problem seems to rear it's ugly head on a regular basis.
The value assigned to an infinite series (if it converges) the limit of the sequence of partial sums as n-----> inf. if the limit exists. lim as n---inf.[(2^n - 1]/2^n = 1 so therefore for the series = 1. Stop torturing yourselves.
There is a difference between n----> inf and actually adding up all of the infinite number of terms
Try watching this Mathologer Video
https://www.youtube.com/watch?v=SDtFBSjNmm0
and you can argue with Bukard. I doubt if you would win as he knows what he is talking about.
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