If x be the greatest integer less than or equal to x , then ∑ n = 8 100 - 1 n n 2 is equal to:

Let S = ∑ n = 8 100 - 1 n · n 2 Therefore, S = 4 - 5 + 5 - 6 + 6 + … - 50 + 50 ⇒ S = 4 .

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MathematicsFunctionsPeriodicityMedium2 minPYQ_2021

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If $[x]$ be the greatest integer less than or equal to $x,$ then $\sum_{n = 8}^{100} [\frac{{(- 1)}^{n} n}{2}]$ is equal to:

Answer:

Solution:

Let $S = \sum_{n = 8}^{100} [\frac{{(- 1)}^{n} \cdot n}{2}]$

Therefore, $S = 4 - 5 + 5 - 6 + 6 + \dots - 50 + 50$

$\Rightarrow S = 4 .$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Periodicity

⏱ 2mℹ️ Source: PYQ_2021

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