Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Proving (n+1) Sum of Squares with Induction
Reply to thread
Message
[QUOTE="mikky05v, post: 4678277, member: 444256"] [h2]Homework Statement [/h2] Prove by induction that the sum of the first n "squares" is n(n+1)(2n+1)/6 In other words prove ([itex]\forall[/itex]n) P(n) where P (n) is [itex]\sum[/itex][itex]^{n}_{i=1}[/itex]¡[itex]^{2}[/itex]=[itex]\frac{n(n+1)(2n+1)}{6}[/itex] [h2]Homework Equations[/h2] This is just not clicking for me right now. I have no idea if i am just epic failing at factoring or doing something else wrong. [h2]The Attempt at a Solution[/h2] I did the base case and proved P (1) true easily enough. Induction case: suppose P (k), then [itex]\sum[/itex][itex]^{k}_{i=1}[/itex]i[itex]^{2}[/itex]=[itex]\frac{k (k+1)(2k+1)}{6}[/itex] show P (k+1) is true, then ∑[itex]^{k+1}_{i=1}[/itex]i[itex]^{2}[/itex]=[itex]\frac{(k+1)(k+1)(2k+1)}{6}[/itex] [itex]\sum[/itex][itex]^{k+1}_{i=1}[/itex]i[itex]^{2}[/itex]=[itex]\sum[/itex][itex]^{k}_{i=1}[/itex]i[itex]^{2}[/itex]+(k+1)[itex]^{2}[/itex] =[itex]\frac{k (k+1)(2k+1)}{6}[/itex] + (k+1)[itex]^{2}[/itex] Now i know i need to get itto work out to the [itex]\frac{(k+1)(k+1)(2k+3)}{6}[/itex] but i can't manage to get itto work out at all. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Proving (n+1) Sum of Squares with Induction
Back
Top