Sum of the series 3 + 5 + 9 + 17 + 33 + … .to n terms is

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Easy2 minQB

MathematicsEasysingle choice

Sum of the series $3 + 5 + 9 + 17 + 33 + \dots$ .to $n$ terms is

Answer:

Solution:

The series can be written as $(2 + 1) + (2^{2} + 1) + (2^{3} + 1) + ...$ . Separating the terms, we get the sum of a geometric progression and $n$ .

Thus, $S_{n} = 2 (2^{n} - 1) + n = 2^{n + 1} - 2 + n$ .

The sum to $n$ terms is $2^{n + 1} + n - 2$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

Loading discussions...