Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Hard2 minPYQ_2020

MathematicsHardstatement

The greatest positive integer $k,$ for which $49^{k} + 1$ is a factor of the sum $49^{125} + 49^{124} + \dots + 49^{2} + 49 + 1,$ is

Answer:

Solution:

This series is a G.P. with first term $49^{125}$ and common ratio $\frac{1}{49}$ .

So, its sum $= \frac{{(49)}^{126} - 1}{48} = \frac{({(49)}^{63} + 1) (49^{63} - 1)}{48}$

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

⏱ 2mℹ️ Source: PYQ_2020

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