NVAMediumJEE Main 2024 · 30 January, Shift 1Sum of Series

Mathematics Question from JEE Main 2024 · 30 January, Shift 1

Let α=12+42+82+132+192+262+...\alpha = 1^2 + 4^2 + 8^2 + 13^2 + 19^2 + 26^2 + ... up to 1010 terms and β=n=110n4\beta = \sum_{n=1}^{10} n^4. If 4αβ=55k+404\alpha - \beta = 55k + 40, then kk is equal to:

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