Answer:
The solution of the given inequality n < 5
Step-by-step explanation:
<u><em>Explanation</em></u>:-
Given inequality
<u><em>Step(i)</em></u>:-
Cross multiplication '4' we get
8 n - 12 < 4 ( n +2)
8 n - 12 < 4 n + 4×2
8 n - 12 < 4 n +8
Subtracting '4 n ' on both sides, we get
8 n - 4 n - 12 < 4 n - 4 n +8
4 n - 12 < 8
<u><em>Step(ii):-</em></u>
Adding ' 12 ' on both sides , we get
4 n -12 + 12 < 8 + 12
4 n < 20
Dividing "4' on both sides , we get
n < 5
The solution is n < 5
<u><em>Conclusion:-</em></u>
The solution of the given inequality n < 5
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.
The answer is to this is 3/4
