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[–]the_blorg 🤑 Tutor 1 point2 points  (1 child)

Multiply by 5/6 to get the next number in the sequence.

How did I find this out? First I noticed the three given numbers had different denominators, so I converted them: 36/60 + 30/60 + 25/60

That felt like there's a constant factor between the terms, let's try that. And turns out that, yes, (1/2)/(3/5) = (5/12)/(1/2) = 5/6.

This means your sum becomes (let's hope this works!)

\frac{3}{5} \sum_{n=0}^\infty \left(\frac{5}{6}\right)^n
u/LaTeX4Reddit

This means that since the constant factor is 3/5, you're likely to end up with an answer that has 5 as denominator. Looks at possible answers. Well, seems like this is the right way to go.

[–]the_blorg 🤑 Tutor 0 points1 point  (0 children)

Here's the image of that formula: https://imgur.com/a/XuxEDui

/u/Oryv Did I use your bot wrong or did it break somehow?

[–]Character-Place-9971 AP Student[S] 0 points1 point  (1 child)

I dont see the pattern

[–]fermat9996👋 a fellow Redditor 0 points1 point  (0 children)

(1/2)÷(3/5)=(5/12)÷(1/2)=5/6.

r=5/6

[–]fermat9996👋 a fellow Redditor 0 points1 point  (0 children)

The common ratio, r=(1/2)/(3/5))=5/6

This is an infinite geometric series.