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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 |