The sum to n terms of the series 2 1 + 4 3 + 8 7 + 16 15 + ………… is

2 1 + 4 3 + 8 7 + 16 15 + … = = ( 1 − 2 1 ) + ( 1 − 4 1 ) + ( 1 − 8 1 ) + ( 1 − 16 1 ) + … . n − 1 − 2 1 2 1 { 1 − 2 n 1 } = n − 1 + 2 − n

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMiscellaneous/MixedMedium2 minPYQ_2016

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The sum to $n$ terms of the series $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \dots\dots\dots\dots$ is

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Answer:

Solution:

$\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \dots = = (1 - \frac{1}{2}) + (1 - \frac{1}{4}) + (1 - \frac{1}{8}) + (1 - \frac{1}{16}) + \dots . n - \frac{\frac{1}{2} { 1 - \frac{1}{2 ^{n}} }}{1 - \frac{1}{2}} = n - 1 + 2^{- n}$

Stream:BITSATSubject:MathematicsTopic:Sequence & SeriesSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2016

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