Question

Sum of the series 0.5 + 0.55 + 0.555 + . . . . . . . . . upto n terms is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We have,
$S_n$ = 0.5 + 0.55 + 0.555 + . . . . upto n terms
$=\frac{5}{9}[0.9+0.99+0.999+....nterms]=\frac{5}{9}[(1-\frac{1}{10})+(1-\frac{1}{100})+(1-\frac{1}{1000})+....]=\frac{5}{9}[(1+1+1+....)-(\frac{1}{10}+\frac{1}{{10}^2}+\frac{1}{1063}+....)]=\frac{5}{9}[n-\frac{1}{10}\frac{(1-\frac{1}{{10}^n})}{1-\frac{1}{10}}]=\frac{5}{9}[n-\frac{1}{10}\times \frac{10}{9}(1-\frac{1}{{10}^n})]=\frac{5}{9}[n-\frac{1}{9}(1-\frac{1}{{10}^n})]$