Apply Pascal's Identity to simplify the combination terms.

Physics
Apply Pascal's Identity to simplify the combination terms.

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Step 1: Apply Pascal's Identity to simplify the combination terms. The given equation is (n+1)C4(n1)C4+6=4n(n+1)C_4 - (n-1)C_4 + 6 = 4n. We use Pascal's Identity: kCr=k1Cr+k1Cr1^kC_r = ^{k-1}C_r + ^{k-1}C_{r-1}. First, apply it to (n+1)C4(n+1)C_4: (n+1)C4=nC4+nC3(n+1)C_4 = ^nC_4 + ^nC_3 Substitute this into the original equation:

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