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EEJ MAIN Mathematics QUESTION #7490
Question 1
The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, … is:
  • \(\frac{7}{81}(179-10^{-20})\)
  • \(\frac{7}{9}(99-10^{-20})\)
  • \(\frac{7}{81}(179+10^{-20})\)✔️
  • \(\frac{7}{9}(99+10^{-20})\)
Correct Answer Explanation
Each term: \(0.7 = \frac{7}{9}(1-10^{-1})\), \(0.77 = \frac{7}{9}(1-10^{-2})\), etc. Sum = \(\frac{7}{9}\sum_{k=1}^{20}(1-10^{-k}) = \frac{7}{9}[20 - \frac{10^{-1}(1-10^{-20})}{1-10^{-1}}] = \frac{7}{9}[20 - \frac{1-10^{-20}}{9}] = \frac{7}{9} \cdot \frac{180-1+10^{-20}}{9} = \frac{7}{81}(179+10^{-20})\).