Explain why exactly.

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

1. Explain why

0.\overline{9} = 1

exactly. (1) Explain why

0.\overline{9} = 1

exactly. (2) Show that if

u_n = \frac{9}{10^n}

, then

S_n = 1 - \frac{1}{10^n}

. (3) On a graph, plot the points

(n, u_n)

and

(n, S_n)

for

n = 1, 2, \dots, 10

. Connect each set of points with a smooth curve.