Help a level maths urgent
Help I don’t get why a is one and r is cos theta I understand the rest of the q just not that part which restricts me to one mark 😭
(edited 10 months ago)
We agree this is a geometric series, right?
So in this case, when using the sum of GS formula, a/(1-r), a is the first term, and r is the common ratio.
Usually, if you aren't sure, just write out the series (instead of in sigma notation) until you see what's happening.
For instance, this series reads
"cos(theta)^0 = 1, cos(theta)^1, cos(theta)^2, cos(theta)^3,..."
Can you see better what's the first term and what's the common ratio?
So in this case, when using the sum of GS formula, a/(1-r), a is the first term, and r is the common ratio.
Usually, if you aren't sure, just write out the series (instead of in sigma notation) until you see what's happening.
For instance, this series reads
"cos(theta)^0 = 1, cos(theta)^1, cos(theta)^2, cos(theta)^3,..."
Can you see better what's the first term and what's the common ratio?
(edited 10 months ago)
Original post by tonyiptony
We agree this is a geometric series, right?
So in this case, when using the sum of GS formula, a/(1-r), a is the first term, and r is the common ratio.
Usually, if you aren't sure, just write out the series (instead of in sigma notation) until you see what's happening.
For instance, this series reads
"cos(theta)^0 = 1, cos(theta)^1, cos(theta)^2, cos(theta)^3,..."
Can you see better what's the first term and what's the common ratio?
So in this case, when using the sum of GS formula, a/(1-r), a is the first term, and r is the common ratio.
Usually, if you aren't sure, just write out the series (instead of in sigma notation) until you see what's happening.
For instance, this series reads
"cos(theta)^0 = 1, cos(theta)^1, cos(theta)^2, cos(theta)^3,..."
Can you see better what's the first term and what's the common ratio?
But how do I know the value of theta
I was trying write out the sequence but I can’t do
cos(theta)^1 in my calc so idk what a or r is
Original post by Alevelhelp.1
But how do I know the value of theta
I was trying write out the sequence but I can’t do
cos(theta)^1 in my calc so idk what a or r is
I was trying write out the sequence but I can’t do
cos(theta)^1 in my calc so idk what a or r is
you dont know what theta is to start with, but the series starts with n=0 so 1st term (a) must be 1. Set up an eq in a and r for infinite sum, solve for r, then work out what theta must be
Original post by Alevelhelp.1
But how do I know the value of theta
I was trying write out the sequence but I can’t do
cos(theta)^1 in my calc so idk what a or r is
I was trying write out the sequence but I can’t do
cos(theta)^1 in my calc so idk what a or r is
We don't know what theta is! That's what we are trying to find in the end, right?
But still, the common ratio is just whatever is multiplied to the previous term. That could be or not be a number, as long as it's the same for the entire series.
Even though we don't know what x is, we can still say the series,
1, x, x^2, x^3,...
is a GS with first term 1 and common ratio x. It doesn't need to have numbers!
(edited 10 months ago)
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