when they say write out each sum would the answer be 5, 7, 9, ... , 2k+3
#summation notation
pallid summit
regal wharfBOT
coral frigate
You have to write like this (2(1)+3) +(2(5)+3)+ (2(7)+3)+ (2(9)+3)=??
pallid summit
then what number would i stop at
coral frigate
Simplify the number @pallid summit
pallid summit
what do you mean?
coral frigate
I mean simplify the expression
Whatever, The number would be 56.
What grade are you study?
drifting plover
when they say write out each sum would the answer be 5, 7, 9, ... , 2k+3
= 2(1)+3+2(2)+3+2(3)+3+...2(n)+3
=2(1+2+3+...+n)+3(n)
if you know AP
then,
sum of first n natural numbers is n(n+1)
so,
1+2+3+...+n=n(n+1)/2
so our expression equals to
=2(n(n+1)/2)+3n
=n(n+1)+3n
=n^2+n+3n
so answer is
$n^2+4n$
smoky spireBOT
Pro_Hecker
drifting plover
and btw by write out each sum they meant to solve sum for questions 17-20
type .close to close this thread if you're problem has been resolved
pallid summit
= 2(1)+3+2(2)+3+2(3)+3+...2(n)+3
=2(1+2+3+...+n)+3(n)
if you know AP
then,
sum o...
so then i would just write n^2 + 4n?
olive solar
then what number would i stop at
n is an ambiguous number
As you keep adding things up, n will be the last number you use in the summation
The people here are giving examples of numbers you can use to represent n. But if you go all the way to n sums, there's a pattern that will appear.
But to answer your original question:
You don't use commas for this. Since you're doing a sum, use + instead
drifting plover
i gave answer its n^2 +4n
olive solar
i gave answer its n^2 +4n
Sure, but I don't think the OP fully understand why so I'm explaining the concept to her
pallid summit
then how would you write the sum for
would the concept be the same as the previous one?
olive solar
would the concept be the same as the previous one?
Yeah, except here you begin at 2 instead of 1
pallid summit
how would you include ln k into the sum?
olive solar
You can imagine a big parenthesis that covers everything to the right of the sum symbol
So you can start with $$(-1)^2 \ln{2}$$
plus the next number + the number after that
smoky spireBOT
Mellow
pallid summit
but n is the variable on top so the calculations would continue to go on..?
olive solar
Yeah it would continue to go until it reaches n
pallid summit
so then how would i calculate the sum?
olive solar
There's a chance that you can't
You might have to leave it terms of n
For stuff that has variables like this, there's going to be a pattern that the sum follows. If you find that pattern, you can turn it into an equation
It can get closer and closer to a single value
We say it "converges" if it does
There are times where you can't tho. We say it "diverges".
At that point, you have to write the pattern with some ... in the middle to say this goes on for a while
pallid summit
we havent gotten to the divergent convergent part so i think the teacher wants us to write an equation representing the sum
but im not sure how or where to start
olive solar
Ahh okay, I think Ik where you're at then
Well you start with $$(-1)^2 \ln{2} + ... $$ what comes after?
smoky spireBOT
Mellow
pallid summit
(-1)^3 ln3
pallid summit
(-1)^4 ln4
olive solar
Right you got it
So what you have rn is $$(-1)^2 \ln(2) + (-1)^3 \ln(3) + (-1)^4 \ln(4) + ... $$
smoky spireBOT
Mellow
olive solar
If you keep doing this until n, what does it look like?
Aka what do you get for the last one?
olive solar
Yes, just waiting on the OP's response
pallid summit
(-1)^k ln(k)??
drifting plover
Yes, just waiting on the OP's response
can you DM me the answer
olive solar
(-1)^k ln(k)??
Close! But remember that k becomes the number at the top at the end
pallid summit
so replace k with n?
olive solar
can you DM me the answer
Sure, but it's simpler than you think
pallid summit
(-1)^n ln(n)
olive solar
(-1)^n ln(n)
Exactly!
So then wouldn't the summation look like $$(-1)^2 \ln(2) + (-1)^3 \ln(3) + (-1)^4 \ln(4) + ... + (-1)^n \ln(n)$$
smoky spireBOT
Mellow
olive solar
it wouldnt be like the first one?
It can't be like the first one cause the number only keeps on getting bigger
smoky spireBOT
Pro_Hecker
pallid summit
but the first one is similar since the top number/variable is n
drifting plover
there is no solution
olive solar
but the first one is similar since the top number/variable is n
Yeah that's true but that's because the first one had a pattern to it
regal wharfBOT
Solved