# SOLUTION: use mathematical induction to prove that 1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6 for all positive integral values of n

Algebra ->  Algebra  -> Equations -> SOLUTION: use mathematical induction to prove that 1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6 for all positive integral values of n      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Equations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Equations Question 229820: use mathematical induction to prove that 1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6 for all positive integral values of nAnswer by solver91311(16868)   (Show Source): You can put this solution on YOUR website! prove 1. Show that is true for and 2. Assume is true for some positive integer , then show the relationship is true for , namely that: First note that: which can be written: because we assumed the relationship to be true for some positive integer . But (Verification of the previous step is left as an exercise for the student) And (Verification of the previous step is also left as an exercise for the student) Therefore, if the statement is true for some , it must be true for . Since it was proven true for , it must be true for , then it must be true for ... John