A limit problem i have tried for hours now and just cannot wrap my head around
Solution is apparently (1 + x)/(1 - x)^2
any help greatly appreciated,
thanks
jacs
We are adding all of these together. So let us add them in a convenient way.
First we add the left-most coloums together:
Second we add the next left-most coloums together:
Third we add the next left-most colums together:
And so on....
So in total we need to add,
I am going to add and subtract to make it an easier form.
Factor again,
Hello, jacs!
Add the stack of equations . . .
Observe that:
. .
.
By studying the arrangement, or otherwise, find in simplest algebraic form,
. . an expression for the limit of the series: .
Solution: .
The left side is: .
The right side is: .
. . . . . . . . . . .
Factor: .
. . . .
The expressions in parentheses are geometric series:
. . first term , common ratio
Their sum is: .
Hence, we have: .
. . which simplifies to: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Another solution . . . (They did say "otherwise", right?)
We are given: .
Multiply by
Subtract: .
. . . . . . .
So we have : .
Therefore: .