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Build a Geometric Series

A series is formed by adding terms. Here, each term is multiplied by a common ratio r = {{s1.r}}.

Next Term =
Previous × {{s1.r}}
?

Identify the Parts

To sum a finite geometric series, we need the first term (a), ratio (r), and number of terms (n).

Given Series:
{{t}} +
First Term (a)
{{s2.slots.a}}
Ratio (r)
{{s2.slots.r}}
Terms (n)
{{s2.slots.n}}
Drag values to match
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Approaching Infinity

What happens when we add forever? Let and .

Sum = 1
Sum of first {{s3.n}} terms:
{{ s3DecimalValue }}
It gets infinitely close to 1!
1

To Infinity and... Beyond?

An infinite series only has a finite sum (converges) if the ratio |r| < 1. Otherwise, it explodes (diverges).

touch_app Tap ALL series that CONVERGE
Diverges! (|r| ≥ 1)
Missed one!

The Final Calculation

Use the formula for an infinite sum:

Find the exact sum:
Dial in the answer
{{ s5.ans }}
Not quite. Find 'a' and 'r' first!
🎉

Master of Series!

You've successfully built, analyzed, and calculated geometric series, even out to infinity!