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If (a_n=n^3), what is the formula for (a_n-a_{n-1})?यदि (a_n=n^3) है तो (a_n-a_{n-1}) का सूत्र क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(3n^2-3n+1\)\(3n^2-3n+1\)
Here, \(a_{n-1}=(n-1)^3\). Therefore, \(a_n-a_{n-1}=n^3-(n-1)^3=n^3-(n^3-3n^2+3n-1)=3n^2-3n+1\). Hence, option D is correct. Option A is the result of \((n+1)^3-n^3\), not of the given difference. Exam tip: for the previous term, always replace \(n\) with \(n-1\).यहाँ \(a_{n-1}=(n-1)^3\) होगा। अतः \(a_n-a_{n-1}=n^3-(n-1)^3=n^3-(n^3-3n^2+3n-1)=3n^2-3n+1\)। इसलिए विकल्प D सही है। विकल्प A, \((n+1)^3-n^3\) का परिणाम है, न कि दिए गए अंतर का। परीक्षा टिप: पिछले पद के लिए \(n\) के स्थान पर हमेशा \(n-1\) रखें।
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