Three Decisions Hiding in One Fraction

You'll learnwhere the closed form for a geometric sum comes from and why the convergence condition is about one power, to take the numerator from the first term actually present rather than from the coefficient out front, to find the ratio by dividing consecutive terms whatever the notation is doing, and to spot the formula returning a confident answer to a series it does not apply to.

A geometric series is the first one whose sum you can write down, and the fraction that does it is three decisions compressed into one expression: does the series converge at all, which term is the numerator, and which number is the ratio. Each fails on its own, and a wrong answer looks exactly like a right one. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · THREE DECISIONS IN ONE FRACTION · v2

Check the ratio, take the first term present, then divide

Before you start

What you're looking at

One panel whose bottom axis counts whole steps. Pink stems are the terms, violet dots are the running total, and a lime rule is the sum the question asks for.

The question

Four rival answers get drawn as heights too, and every one of them is correct — for a different series.

Step 1 / 12