EasyLimits

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.6 Limits, #1 · Calculus · Limits

(g)

What is $a_{n}$ and what is the limit $L$ ? After which $N$ is $∣ a_{n} - L ∣ < \frac{1}{10}$ ? (Calculator allowed)

(a) $- 1, + \frac{1}{2}, - \frac{1}{3}, \dots$

(b) $\frac{1}{2}, \frac{1}{2} + \frac{1}{4}, \frac{1}{2} + \frac{1}{4} + \frac{1}{8}, \dots$

(c) $\frac{1}{2}, \frac{2}{4}, \frac{3}{8}, \dots, a_{n} = n / 2^{n}$

(d) $1.1, 1.11, 1.111, \dots$

(e) $a_{n} = n n$

(f) $a_{n} = n^{2} + n - n$

(g) $1 + 1, (1 + \frac{1}{2})^{2}, (1 + \frac{1}{3})^{3}, \dots$

~5 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.6 Limits, #1

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.