If ∑ α = 4 n + 3 4 ( α − 3 ) = A n 2 + B n + C , then find the value of A + B − C

∑ α = 4 n + 3 4 ( α − 3 ) = A n 2 + B n + C ⇒ ∑ α = 1 n 4 α = A n 2 + B n + C ⇒ 2 n ( n + 1 ) = A n 2 + B n + C ⇒ A + B + C = 4

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MathematicsSequence & SeriesA.P.Easy2 minQB

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If $\sum_{α = 4}^{n + 3} 4 (α - 3) = A n^{2} + B n + C$ , then find the value of $A + B - C$

Answer:

Solution:

$\sum_{α = 4}^{n + 3} 4 (α - 3) = A n^{2} + B n + C \Rightarrow \sum_{α = 1}^{n} 4 α = A n^{2} + B n + C$

$\Rightarrow 2 n (n + 1) = A n^{2} + B n + C$

$\Rightarrow A + B + C = 4$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.P.

⏱ 2mℹ️ Source: QB

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