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Find the sum to n-terms of given sequence:1.6 + 1.66 + 1.666+….... |
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Answer» Let S = 1.6 + 1.66 + 1.666 + ..... + n terms = (1 + 0.6) + (1 + 0.6 + 0.06) + (1 + 0.6 + 0.06 + 0.006) + ......+ n terms = (1 + 1 + ..... + 1)(n times) + (\(\frac{6}{10}\) + \(\frac{6}{10}\) + \(\frac{6}{10}\) + .....+\(\frac{6}{10}\)) (n times) + (\(\frac{6}{100}\) + \(\frac{6}{100}\) + \(\frac{6}{100}\) + .... + \(\frac{6}{100}\)) ((n-1) times) + (\(\frac{6}{10^3}\) + \(\frac{6}{10^3}\) + \(\frac{6}{10^3}\) + .... + \(\frac{6}{10^3}\))((n-2) times) + .... + \(\frac{6}{10^n}\) = n + \(\frac{6n}{10}\) + \(\frac{6(n-1)}{100}\) + .... + \(\frac{6}{10^n}\) |
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