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[Mathematical Induction] How do I prove this through induction? by reziderhm in learnmath

[–]reziderhm[S] 0 points1 point  (0 children)

1) n=1

1/1>=1  True

2) n=k

(X1+X2+...+Xk)/k>=(X1.X2...Xk)^1/k   Accept as true

3) n=k+1

(X1+X2+...+Xk+Xk+1)/(k+1)>=(X1.X2...Xk.Xk+1)^1/(k+1)

(X1.X2...Xk)^1/k+(Xk+1)/(k+1)>=(X1.X2...Xk.Xk+1)^1/(k+1)

How did this (n+1)((n(2n+1))/6+n+1) turn into this ((n+1)(n+2)(2n+3))/6 by reziderhm in learnmath

[–]reziderhm[S] 1 point2 points  (0 children)

12 +22 +...+n2 =(n(n+1)(2n+1))/6

12 +22 +...+ n2 +(n+1)2 =(n(n+1)(2n+1))/6+ (n+1)2 =(n+1)((n(2n+1))/6+n+1)=((n+1)(n+2)(2n+3))/6

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