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Home » Ishmael Exposed: The Shocking Truth Behind the Enigmatic Character You’ve Never Known! - AMAZONAWS

Ishmael Exposed: The Shocking Truth Behind the Enigmatic Character You’ve Never Known! - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 Solving \( 1 = A(k+1) + Bk \), we equate coefficients:

📌 \( A + B = 0 \)

📌 \( A = 1 \)

📌 Thus, \( B = -1 \). So,

📌 The series becomes telescoping:

📌 All intermediate terms cancel, leaving:

📌 - \frac{1}{51}

📌 = \frac{51 - 1}{51} = \frac{50}{51}

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Compute up to $a_8$:
a_3 = a_2 + a_1 = 3 + 2 = 5 \\
a_4 = a_3 + a_2 = 5 + 3 = 8 \\
a_5 = a_4 + a_3 = 8 + 5 = 13 \\
a_6 = a_5 + a_4 = 13 + 8 = 21 \\
a_7 = a_6 + a_5 = 21 + 13 = 34 \\
a_8 = a_7 + a_6 = 34 + 21 = 55
So, number of 8-digit numbers **without** consecutive 3s is 55.
Thus, the number **with** at least one pair of consecutive 3s is:
- 55 = \boxed{201}

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