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

Printable View

- June 8th 2007, 02:44 AMjacsSeries problem with limiting sum
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 - June 8th 2007, 07:17 AMThePerfectHacker
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,

- June 8th 2007, 07:22 AMSoroban
Hello, jacs!

Quote:

Observe that:

. .

.

By studying the arrangement, or otherwise, find in simplest algebraic form,

. . an expression for the limit of the series: .

Solution: .

**Add**the stack of equations . . .

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: .

- June 8th 2007, 07:39 AMjacs
thanks to both of you. i dont think i ever woudl have figured that one out in a milion years. Going ot have a study of all the different methods and see which one i can try to replicate without giving myself and annureism.

thanks, you guys rock!