d. 1. (2 x 4-8 pts) Find the shortest possible closed formula equal to each. Allowed...

 

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d. 1. (2 x 4-8 pts) Find the shortest possible closed formula equal to each. Allowed key stroke: binomial coefficient a. (V) \binom(x)(y) ()-(2)+(1) - ... + (-1) +1 (n) : b. (0+ n) + (1 + n) + ( + n). +-+ (272) C. 2 Hint: Write it down with the sigma notation. Use two binomial coefficient identities learned in class. Which are they? 2 2 1 (4) + 2 (2) + 3 (3) + + n (m) Hint: Use three learned binomial coefficient identities. n-m 1 n (-) (m=1) n- m d. 1. (2 x 4-8 pts) Find the shortest possible closed formula equal to each. Allowed key stroke: binomial coefficient a. (V) \binom(x)(y) ()-(2)+(1) - ... + (-1) +1 (n) : b. (0+ n) + (1 + n) + ( + n). +-+ (272) C. 2 Hint: Write it down with the sigma notation. Use two binomial coefficient identities learned in class. Which are they? 2 2 1 (4) + 2 (2) + 3 (3) + + n (m) Hint: Use three learned binomial coefficient identities. n-m 1 n (-) (m=1) n- m