# What does it mean when there is a number to the left of a summation sigma?

Trying to read Simple Wikipedia's Mathematical Induction article:

https://simple.wikipedia.org/wiki/Mathematical_induction

In many of the images, like this one:
https://wikimedia.org/api/rest_v1/media/math/render/svg/8aca5140d2bef31cc6ec27c34ace175533d0685d

There is a 2 to the right sorry, left of the summation symbol. What does it mean?

• It's just a multiplicative factor. You should read it as "2 times the sum of...". – Hubble Oct 3 '16 at 19:00
• 2 * the sum of all of those numbers leading up to n (aka, 2 * n)? It's not really clicking with me... – user156964 Oct 3 '16 at 19:07
• $2 \times \left(\sum_{k=1}^n k\right) = n(n+1)$. – Hubble Oct 3 '16 at 19:11
• Ok, so the idea is that you keep adding up until what you're adding is the number n. And that first image I linked is rewritten from wikimedia.org/api/rest_v1/media/math/render/svg/… with the 1/2 taken from the left and added as a times 2 on the right. Thanks. – user156964 Oct 3 '16 at 19:18

If you have $$a\sum_{b=1}^{c}d$$, that means you multiply $$a$$ by $$\sum_{b=1}^{c}d$$. Thus, you take $$2$$ and multiply it by $$\sum_{k=1}^{n}k$$.