Question

32. The series 1+10-1+10-2 +10-3... to mois do (a) 9/10 (b) 1/10 (c) 10/9 (d) none of these​

Answer 1

$option : (c) \: \frac{10}{9}$

Step-by-step explanation:

$Given, \: \: the \: \: series \: \: 1 + {10}^{ - 1} + {10}^{ - 2} + {10}^{ - 3} + ...to \: \infty \\ then, \: \: a = 1 \: \: \: and \: \: \: r = \frac{1}{10} \\ we \: \: know \: \: \boxed{Sum \: \: of \: \: infinite \: \: terms \: \: of \: \: G.P = \frac{a}{1 - r} } \\Now, \: \: putting \: \: values \\ then, \: \: \: sum = \frac{1}{1 - \frac{1}{10} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{ \frac{9}{10} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{10}{9}$