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The value of $-{}^{15}C_1 + 2 \cdot {}^{15}C_2 - 3 \cdot {}^{15}C_3 + \ldots - 15 \cdot {}^{15}C_{15} + {}^{14}C_1 + {}^{14}C_3 + {}^{14}C_5 + \ldots + {}^{14}C_{11}$ is:
(1) $2^{14}$ (2) $2^{13} - 13$ (3) $2^{16} - 1$ (4) $2^{13} - 14$
$S_1 = 0$, $S_2 = 2^{13} - 14$.
BETA
