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Home » \textLCM = 2^3 \times 3^1 = 8 \times 3 = 24 - Abu Waleed Tea

\textLCM = 2^3 \times 3^1 = 8 \times 3 = 24 - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Now compute the difference:
E(t+1) - E(t) = a(t+1)^2 + b(t+1) - (at^2 + bt) = a(2t+1) + b = 2at +...
Set equal to $ 2t + 1 $:
2at + (a + b) = 2t + 1.
2a = 2 \Rightarrow a = 1, \quad a + b = 1 \Rightarrow 1 + b = 1 \Right...
Thus, $ E(t) = t^2 $.
Then $ E(10) = 10^2 = 100 $.
Alternatively, recognize the recurrence as the discrete analog of deri...
E(1) = E(0) + 1 = 1, \quad E(2) = 1 + (2\cdot1 + 1) = 1 + 3 = 4, \quad...
So $ E(n) = \sum_{k=0}^{n-1} (2k + 1) = n^2 $, since sum of first $ n...

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