Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
giovkast
Group Title
solve with full induction:
sum_{k=1}^{n} k^2 = 1/6n(n + 1)(2n+1)
 one year ago
 one year ago
giovkast Group Title
solve with full induction: sum_{k=1}^{n} k^2 = 1/6n(n + 1)(2n+1)
 one year ago
 one year ago

This Question is Closed

giovkast Group TitleBest ResponseYou've already chosen the best response.0
\[\sum_{k=1}^{n} k^2 = 1/6n(n + 1)(2n+1)\]
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
first step: n = 1: \[\sum_{k=1}^{1}k^2=1^2 = 1,\quad (1/6)(1)(2)(3) = 1\]
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
step 2: induction process. assume true for n=s \[\sum_{k=1}^{s}=1^2+2^2+\cdots +s^2=(1/6) s(s+1)(2s+1)\] show the formula is true for n = s+1 \[\sum_{k=1}^{s+1}=1^2+2^2+\cdots + s^2 + (s+1)^2\]\[=\left[ (1/6)s(s+1)(2s+1) \right]+(s+1)^2\]
 one year ago

giovkast Group TitleBest ResponseYou've already chosen the best response.0
here i got stuck
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
simplify the expressions, then factor. if you get \[(1/6)(s+1)(s+2)(2s+3)\] then you're in the right track.
 one year ago

giovkast Group TitleBest ResponseYou've already chosen the best response.0
\[1/3n^3+3/2n2+3/2n+1\]
 one year ago

giovkast Group TitleBest ResponseYou've already chosen the best response.0
i got this, don't know where i went wrong
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
you need to add \[\frac{s(s+1)(2s+1)}{6}+\frac{(s+1)^2}{1}=\frac{s(s+1)(2s+1)+6(s+1)^2}{6}\] \[=\frac{(s+1)[s(2s+1)+6(s+1)]}{6}=\frac{(s+1)(2s^2+7s+6)}{6}=\frac{(s+1)(2s+3)(s+2)}{6}\] we need to show that this is the same as n=s+1 in the original ie \[\frac{(\color{red}{s+1})(2\color{red}{(s+1)}+1)(\color{red}{s+1}+1)}{6}\]TRUE
 one year ago

giovkast Group TitleBest ResponseYou've already chosen the best response.0
thank you very much
 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.