The sum of the series 1 2 + 2. 2 2 + 3 2 + 2. 4 2 + 5 2 + 2. 6 2 + … .. + 2 ( 2 m ) 2 is

The sum of the given series 1 2 + 2. 2 2 + 3 2 + 2. 4 2 + 5 2 + 2. 6 2 + …… .. + 2 ( 2 m ) 2 is 2 2 m ( 2 m + 1 2 ⩽ m ( 2 m + 1 2 )

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MathematicsSequence & SeriesSpecial sequences/seriesHard2 minPYQ_2012

MathematicsHardstatement

The sum of the series $1^{2} + 2. 2^{2} + 3^{2} + 2. 4^{2} + 5^{2} + 2. 6^{2} + \dots .. + 2 (2 m)^{2}$ is

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Answer:

Solution:

The sum of the given series $1^{2} + 2. 2^{2} + 3^{2} +$ $2. 4^{2} + 5^{2} + 2. 6^{2} + \dots\dots .. + 2 (2 m)^{2}$ is $\frac{2 m ( 2 m + 1 ^{2}}{2} ⩽ m (2 m + 1^{2})$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: PYQ_2012

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