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The sum of n terms the series 1 + 1 + 1 + 1 + ..... is 2 2² 2³
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2n - 1 2n - 1 -
2n - 1 - 1 2n - 2 - 2 – 2n
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2n - 1 2n
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Correct Option: A
As per the given series ,
| 1 + | + | + | + ....... n to n terms is a Geometric series | |||
| 2 | 2² | 2³ |
whose first term (a) is 1 and the commonratio (r) is
1 / 2 .
Using the given formula ,
| Sn = | |
| 1 - r |
| Sn = | ![]() | 1 - | ![]() | |
| 2n | ||||
| 1 - | ||||
| 2 | ||||
| Sn = | ![]() | ![]() | ||
| 2n | ||||
| 2 | ||||
| Sn = 2. | ![]() | ![]() | = | ||
| 2n | 2n - 1 |

