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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsGeneral (Definition,type and special type)Medium2 minQB

MathematicsMediumsingle choice

Let $S = \sum_{r = 1}^{117} \frac{1}{2 [ r ] + 1}$ where [.] denotes the greatest integer function. The value of S is

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Solution:

$[117] = 10$ ; If $r \in [n^{2}, (n + 1)^{2}) : n \in N$ then $[r] = n$

The interval $[n^{2}, (n + 1)^{2})$ has $2 n + 1$ integers $S = \frac{1}{2.1 + 1} .3 + \frac{1}{2.2 + 1} .5 + \dots . + \frac{1}{2.9 + 1} .19 + \frac{1}{2.10 + 1} .18 = 9 + \frac{18}{21} = \frac{69}{7}$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:General (Definition,type and special type)

⏱ 2mℹ️ Source: QB

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