DeepSeries

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.1 The Geometric Series, #44 · Calculus · Series

How many terms of the series … are needed before the first…

How many terms of the series $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots$ are
needed before the first decimal place doesn't change? Which
power of $\frac{1}{4}$ equals the $100$ th power of $\frac{1}{2}$ ? Which power $1/ a^{n}$ equals
$1/ 2^{100}$ ?

~11 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.1 The Geometric Series, #44

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.