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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:
The number of cards Paul had at the beginning was 64 cards
Step-by-step explanation:
Here we have a word problem as follows
Paul traded 13 baseball card to Dan for 4 new packs of 6 card each
Number of cards received from Dan = 6 × 4 = 24
Number of cards traded to Dan = 13
Net number of cards traded = 24 - 13 = 11
Total number of cards Paul now has = 75 cards
Therefore since Paul gained 11 cards to make his total number of cards = 75, then;
The initial amount of cards Paul had = 75 - 11 = 64 cards.
