Not an expertise on infinite sums but the most straightforward explanation is that infinity isn't a number.
Let's see if there are anything we missed:
∞
Σ 2^n=1+2+4+8+16+...
n=0
We multiply (2-1) on both sides:
∞
(2-1) Σ 2^n=(2-1)1+2+4+8+16+...
n=0
And we expand;
∞
Σ 2^n=(2+4+8+16+32+...)-(1+2+4+8+16+...)
n=0
But now, imagine that the expression 1+2+4+8+16+... have the last term of 2^n, where n is infinity, then the expression of 2+4+8+16+32+... must have the last term of 2(2^n), then if we cancel out the term, we are still missing one more term to write:
∞
Σ 2^n=-1+2(2^n)
n=0
If n is infinity, then 2^n must also be infinity. So technically, this goes back to infinity.
Although we set a finite term for both expressions, the further we list the terms, they will sooner or later approach infinity.
Yep, this shows how weird the infinity sign is.
Answer:
DBA =110 degree
Step-by-step explanation:
angle DBA is central angle
central angle = arc angle = 110 degree
Well, you only listed three pieces so far. But I can already see a
pattern emerging from those three.
Of course, the next piece might return to 1-1/2 inches. I mean,
the pattern can't just keep on going and increasing forever or
Cody would eventually wind up with pieces that are a mile long.
It must eventually return to 1-1/2 inches and start over from there.
From the first piece to the second one, and from the second one
to the third one, the increase is 5/16 inch both times. So if the
pattern is more than three pieces long before it starts over from
1-1/2, then the next piece is
(2-1/8 + 5/16) = (2-2/16 + 5/16) = 2-7/16 inches .
