For 0 ≤ i < j ≤ n , let S = ∑∑ ( i + j ) ( ( i n ) 2 + ( j n ) 2 + ( i n ) ( j n ) ) . Then S equals

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremProperties of Binomial coefficientsHard2 minQB

MathematicsHardsingle choice

For $0 \leq i < j \leq n$ , let $S = \sum\sum (i + j) ((i n)^{2} + (j n)^{2} + (i n) (j n))$ . Then $S$ equals

Answer:

Solution:

Replace $i, j$ by $n - i, n - j$ and add the two forms. Using Vandermonde's identity and symmetry gives $2 S = n {(2 n - 1) (n 2 n) + 4^{n}}$ .

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Properties of Binomial coefficients

⏱ 2mℹ️ Source: QB

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