Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
SOMEONE PLEASE HELP I'M ALMOST DONE.
Use mathematical induction to prove the statement is true for all positive integers n.
8 + 16 + 24 + ... + 8n = 4n(n + 1)
 one year ago
 one year ago
SOMEONE PLEASE HELP I'M ALMOST DONE. Use mathematical induction to prove the statement is true for all positive integers n. 8 + 16 + 24 + ... + 8n = 4n(n + 1)
 one year ago
 one year ago

This Question is Closed

ParthKohliBest ResponseYou've already chosen the best response.1
True for the base case. Now assume that it is true for k, and then prove for k + 1.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Can you find the relationship between those two?
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
Is it supposed to be \[\Large 4n(n+1) \] If that's the case, it must run a bit strangely. \[n=1 \longrightarrow 8 \checkmark \\n=2 \longrightarrow24 \neg\checkmark \]
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Actually, the order of operations first tell you to multiply 4 and \(n\), then \(n +1\)
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
I believe I can't follow you @ParthKohli \[\Large 4n(n+1)=4n^2+4n \] right? and still n=1 > 8 n=2 > 24, or where do I miss something? (which is indeed possible=
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
The question is actually saying \((4 \cdot n) \cdot (n + 1)\)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
It is a series, not a sequence.
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
oh I understand, this is where I misunderstood the problem, thank you.
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
It's not explicit mentioned in the problem set, I have seen such problems as mainly sequences/progressions, in which this would be arithmetic.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Spacelimbus, can you please help the asker? I wish I could, but I am currently on a mobile device and it is hard for me to type.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Now that you know it works for the base case, you assume it holds for the case of "k", and you try to prove it works for "k + 1". So, add 8(k + 1) to both sides: 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4k(k + 1) + 8(k + 1) 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4k^2 + 4k + 8k + 8 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4k^2 + 12k + 8 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4(k^2 + 3k + 2) 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4(k + 1)(k + 2) 8 + 16 + 24 + ... + 8k + 8(k + 1) = 4(k + 1)[(k + 1) + 1] But that is just the same expression we assumed true, but now holding for "k + 1", so this proves the case.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
^ that is simple induction, correct.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
All good now @Pssssst ?
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
The reason this proves the case is because of the way mathematical induction works. The base case has already been shown to be true. Our first "k" is "1" and we have proved it for "k + 1" or "2". "2" becomes our new "k", and by induction, it is proved for "k + 1" or "3", and this process goes on indefinitely. That is why mathematical induction works and why the above proof works.
 one year ago

PssssstBest ResponseYou've already chosen the best response.0
Thank you, everyone! Helped a lot :)
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Glad we were able to help. Thanks for the recognition!
 one year ago

PssssstBest ResponseYou've already chosen the best response.0
@tcarroll010 Do you know much about history?
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.