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SUEvery binomial expansion hides a perfect balance — and most people never see it.In (1+x)ⁿ, if you add up the 1st, 3rd, 5th... term coefficients, and separately add the 2nd, 4th, 6th... term coefficients — they're always equal. Both equal 2^(n−1). Every single time.The proof takes one substitution: plug in x = −1, watch everything cancel, and the symmetry reveals itself.Try it with n = 3 → coefficients are 1, 3, 3, 1 → odd-position sum = 4, even-position sum = 4 → and 2^(3−1) = 4 ✓This is the kind of pattern that looks like magic until you see why it works.Save this if you're studying binomial theorem 📌.
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