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If (f:\mathbb{Z}\to\mathbb{Z}) is given by (f(n)=\frac{n^3-n}{3}), which statement is correct?यदि (f:\mathbb{Z}\to\mathbb{Z}) को (f(n)=\frac{n^3-n}{3}) से दिया गया है, तो कौन सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is a function because (n^3-n) is always divisible by (3)यह फलन है क्योंकि (n^3-n) हमेशा (3) से विभाज्य होता है
Since (n^3-n=n(n-1)(n+1)) is the product of three consecutive integers, it is divisible by (3). For codomain checking, focus on integrality.(n^3-n=n(n-1)(n+1)) लगातार तीन पूर्णांकों का गुणनफल है, इसलिए (3) से विभाज्य है। सहप्रांत जांचने के लिए पूर्णांकता पर ध्यान दें।
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