Geometric sequences question
Can someone please help me solve and explain how did you solve the question below? I am helping my friend and it looks like c2/fp1 stuff but I don't remember doing that with x's and not actual numbers, so is that perhaps c3 or something else? Thanks for explanations.
(edited 11 years ago)
Ignore 1/x for the minute and deal with x+x^2+.... How can you rewrite this? If you can, then you will get a simplified left hand side which can be rearranged and I think will be a quadratic to solve.
Original post by WarriorInAWig
Ignore 1/x for the minute and deal with x+x^2+.... How can you rewrite this? If you can, then you will get a simplified left hand side which can be rearranged and I think will be a quadratic to solve.
I'm sorry I didn't understand what you mean, nor did my friend. How can you ignore 1/x if its first term in the sequence? I tried using a/1-r formula but I would get something like 1/x - 1/x^2 = 3.5 but couldn't solve further, because even if its sort of like quadratic, powers are negative.
1/x + x + x^2 + x^3 +....= 3.5
1/x + x (1 + x + x^2 + x^3 + ...) = 3.5
1/x + x (1/(1-x)) = 3.5
1/x + x/(1-x) = 3.5
I hope that makes more sense.
1/x + x (1 + x + x^2 + x^3 + ...) = 3.5
1/x + x (1/(1-x)) = 3.5
1/x + x/(1-x) = 3.5
I hope that makes more sense.
As it stands you do not have a sequence because there is no common ratio
If you ignore the 1/x (as was suggested) then you have a geometric sequence
If you do not want to ignore it then +1 to both sides
You now have 1/x + 1 + x + x^2 + .... = 4.5
This is a geometric sequence and you can use the sum to infinity rule
If you ignore the 1/x (as was suggested) then you have a geometric sequence
If you do not want to ignore it then +1 to both sides
You now have 1/x + 1 + x + x^2 + .... = 4.5
This is a geometric sequence and you can use the sum to infinity rule
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