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Find \( \sum_{r=0}^{n} \sum_{s=0}^{n} \sum_{t=0}^{n} C_{r} C_{S} C_{t} \) |
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Answer» \(\sum_{r=0}^n \sum_{s=0}^n \sum_{t=0}^n\) Cr Cs Ct = \(\sum_{r=0}^n C_r \sum_{s=0}^n C_s \sum_{t=0}^nC_t\) = 2n. 2n . 2n =23n = (23)n = 8n (∵ \(\sum_{t=0}^n C_t=C_0+C_1+C_2+....+C_n = 2^n\)) |
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