JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f\left( n \right) = \left[ {\frac{1}{3} + \frac{{3n}}{{100}}} \right]n\) , where \([n]\) denotes the greatest integer less than or equal to \(n\). Then \(\sum\limits_{n = 1}^{56} {f\left( n \right)} \) is equal to
- A \(56\)
- B \(689\)
- C \(1287\)
- D \(1399\)
Answer & Solution
Correct Answer
(D) \(1399\)
Step-by-step Solution
Detailed explanation
Let \(f\left( n \right) = \left[ {\frac{1}{3} + \frac{{3n}}{{100}}} \right]n\) where \(\left[ n \right]\) is greatest integer functon, \( = \left[ {0.33 + \frac{{3n}}{{100}}} \right]n\) For \(n = 1,2,....,22,\) we get \(f\left( n \right) = 0\) and for \(n = 23,24,....,55,\) we…
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