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Home » Subtracting consecutive equations eliminates $ d $: - Crosslake

Subtracting consecutive equations eliminates $ d $: - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Since \( x-1 > 0 \), \( x > 1 \), thus \( x = 3 \).
The function \( f(x) = rac{2x^2 - 3x + 1}{x - 1} \) has a removable d...
Factor numerator: \( 2x^2 - 3x + 1 = (2x - 1)(x - 1) \).
So \( f(x) = rac{(2x - 1)(x - 1)}{x - 1} = 2x - 1 \) for \( x
Removing discontinuity, \( f(1) = 2(1) - 1 = 1 \).
A sequence is defined recursively by \( a_1 = 2 \), \( a_{2} = 3 \), a...
\( a_3 = a_2 + 2a_1 = 3 + 2(2) = 7 \)
\( a_4 = a_3 + 2a_2 = 7 + 2(3) = 13 \)
\( a_5 = a_4 + 2a_3 = 13 + 2(7) = 27 \)
\( a_6 = a_5 + 2a_4 = 27 + 2(13) = 53 \)

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