The sum clearly diverges. This is indisputable. The point of the claim above, that

is to demonstrate that a sum of infinitely many terms can be manipulated in a variety of ways to end up with a contradictory result. It's an artifact of trying to do computations with an infinite number of terms.
The mathematician Srinivasa Ramanujan famously demonstrated the above as follows: Suppose the series converges to some constant, call it

. Then

Now, recall the geometric power series

which holds for any

. It has derivative

Taking

, we end up with

and so

But as mentioned above, neither power series converges unless

. What Ramanujan did was to consider the sum

as a limit of the power series evaluated at

:

then arrived at the conclusion that

.
But again, let's emphasize that this result is patently wrong, and only serves to demonstrate that one can't manipulate a sum of infinitely many terms like one would a sum of a finite number of terms.
If she flipped the coin 50 times and it was tail 27 you would time 27 by 4 and it would equal 108 because 50 times 4 is 200
10% off
= $4.80
30% off
= $4.80 x 3
= $14.40
$48 + $14.40
= $62.40
The original price was $62.40
Answer:
<u>50</u>
Step-by-step explanation:
<u>Changing into complex form:</u>
(6 + 8i) * (3 - 4i)
= 18 - 24i + 24i - 32 (i^2)
= 18 - 32(-1)
= 18 + 32
= <u>50</u>
Answer:
y = -2/3 x - 13/3
Step-by-step explanation:
We have one point at (-5,-1) and there is another point at (1,-5)
The slope is
m= (y2-y1)/(x2-x1)
= (-5--1)/(1--5)
= (-5+1)/(1+5)
= -4/6
=-2/3
The point slope form of the equation is
y-y1 = m(x-x1)
y--1 = -2/3(x--5)
y+1 =-2/3( x+5)
Distribute
y+1 = -2/3 x -10/3
Subtract 1 from each side
y +1-1 = -2/3 x -10/3 -1
Get a common denominator
y = -2/3 x -10/3 -3/3
y = -2/3 x - 13/3