An = n times 3 ^ n, find Sn (dislocation subtraction, detailed process)

An = n times 3 ^ n, find Sn (dislocation subtraction, detailed process)

Because Sn = 1 × 3 + 2 × 3 ^ 2 + 3 × 3 ^ 3 + 4 × 3 * 4 +. + n × 3 ^ n 3Sn = 3 ^ 2 + 2 × 3 ^ 3 + 3 × 3 ^ 4 + 4 × 3 ^ 5 +. + (n-1) 3 ^ n + n × 3 ^ (n + 1), 3Sn Sn = n × 3 ^ (n + 1) + (1-2) × 3 ^ 2 + (2-3) × 3 ^ 3 + (3-4) × 3 ^ 4 +. + [(n-1) - n] × 3 ^ n-3 2Sn = n × 3 ^ (n + 1) - 3-3 ^ 2-3 ^ 3 -. - 3 ^ n 2S

Elden Ring Premiere

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