Quantitative Aptitude

Number Series

2,662 Questions
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Number Series Questions

Multiple choice

Find the sum to 90 terms of the series $5+55+555+\cdots\cdots$
  1. $\displaystyle\frac{50}{81}\left[10^{90}-82\right]$
  2. $\displaystyle\frac{50}{81}\left[10^{90}-83\right]$
  3. $\displaystyle\frac{50}{81}\left[10^{90}-80\right]$
  4. $\displaystyle\frac{50}{81}\left[10^{90}-90\right]$
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A Correct answer
Explanation

The series is 5(1 + 11 + 111 + ...) = 5/9 * (9 + 99 + 999 + ...) = 5/9 * [(10-1) + (100-1) + ... + (10^90-1)] = 5/9 * [(10 + 100 + ... + 10^90) - 90]. Using geometric sum: 5/9 * [10(10^90 - 1)/9 - 90] = 50/81 * (10^90 - 1) - 50/9 * 90 = 50/81 * (10^90 - 1 - 81) = 50/81 * (10^90 - 82).