Prove the following identity: 1−2·2+3·4−4·8+· · ·±n·2n−1 = (1−(−2)n(3n+1))/9.?

1−2·2+3·4−4·8+· · ·±n·2n−1 = (1−(−2)n(3n+1))/9.
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