58. DISCOVER - PROVE: Sums of Binomial Coefficients Add each of the first five rows of Pascal's triangle, as indicated. Do you see a pattern? 1+1 = 2 1+ 2 +1 = 2 = 2 1 + 3 + 3 + 1 1+ 4 + 6 + 4 +1 = 2 1+ 5 + 10 + 10 + 5 + 1 = On the basis of the pattern you have found, find the sum of the nth row: () • (;) • ()- +...+ .2. (:) Prove your result by expanding (1 + 1)" using the Binomial Theorem.

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