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Can anyone explain the concept behind this? I just don't get how I should proceed with it? Like each step, why and how is it done?

Prove by induction that $\displaystyle\sum_{i=1}^{n} 2i=(n+1)n$, for every positive integer $n$.

Martin Sleziak
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ABCCode
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There is a proof in here. The standard version of it is $\displaystyle\sum_{i=1}^{n} i=\dfrac{n(n+1)}{2}$

By induction: First, it is valid for $n=1$. Second, suppose that it is correct for $n=k$, i.e., $\displaystyle\sum_{i=1}^{k} i=\dfrac{k(k+1)}{2}$ and by this assumption prove for $n=k+1$.

  • So it's basically just a trick question? Do i need to use that formular for every single question ? since i just can't see where to use i = 1 in it. etc.... – ABCCode Jun 08 '15 at 09:19
  • @ABCCode: Sorry I don't understand what you mean. Definition is $\displaystyle\sum_{i=1}^{n} i=1+2+\dots +n$, if you asked that. For case $n=1$ the equality means $1=\dfrac{1(1+1)}{2}$. –  Jun 08 '15 at 09:28
  • Its just whether the answer to my question is to use that formular (like just paste that formular) or should i insert my own values? Since i cant see where to insert or how to insert my own values.. – ABCCode Jun 08 '15 at 09:35