Recent content by GoGoDancer12

No, its not true because Hn = 1 and (1+1)(1-1) = 0 So, there's no way to prove H1 +H2+...+Hn = (n +1) (Hn - n) is true, right??

I think H1= (1 / n) = 1

How would I know if its correct or not if there is no simple formula for H_n ??

Homework Statement Prove that H1 +H2 +...+Hn = (n +1)(Hn-n)? Homework Equations Hn denotes the nth harmonic number. The nth harmonic number is the sum of 1+1/2+...1/n, which is n / n +1. I'm not really sure if Hn = (1/ n) . Prove by Mathematical Induction Hn denotes the...

Ok, what about the second problem??

I'm lost about showing that (k + 1)^3 + 2(k + 1) is divisible by 3. I expanded the right side of the equation [k^3 + 2k)] /3 = [(k)^3 + (3k)^2 + 5k +3] /3. So, do I replace on the left side [k(k^2 + 2k)] /3 with 3m??

Homework Statement Prove that 3 divides n3 + 2n whenever n is a positive integer. Homework Equations The Attempt at a Solution Basis Step : P(1) : [13 + 2(1) ] /3 [1+2] /3 [3]/3 1 Since 3/3 =1, P(1) is true Inductive Step: [ k3 + 2k...

after expanding the summation some more I got this: 1+1+1+1+1+1+1+2+2+2+2+2+2+2+2+...+m and I'm still lost.

after expanding the summation I got this : 1+1+1+1+1+1+m

exactly :smile:

I have to find the summation formula for floor(K1/3):; and m is the on top of the summation symbol.

omit the second part 2. Homework Equations nLaTeX Code: \\prod j=m aj ...not part of the problem

omit the second part 2. Homework Equations nLaTeX Code: \\prod j=m aj ...not part of the problem

Homework Statement Find a formula for when m \sum k=0 the flooring function of[k1/3 ] ,m is a positive integer. Homework Equations n\prod j=m aj The Attempt at a Solution the flooring function of[k1/3] = K the summation of K is \frac{m(m+1)}{2} There's a table of...