Prove 72 (+1) - (*) a k=0 Hint: Appeal to the binomial theorem. Do not prove...

  

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Prove 72 (+1) - (*) a k=0 Hint: Appeal to the binomial theorem. Do not prove by induction. (1 point) 10b) Prove '() k = n.2n-1 Hint: Take the derivative of both sides of 10a) with respect to x. Now, set x = 1. (2 points) 10c) Prove (*) (7) = n(n+1). 2n-2 k k=1 Hint: Continue with the second derivative of 10a) and proceed as before. The result from 10b) may be useful. (2 points) Prove 72 (+1) - (*) a k=0 Hint: Appeal to the binomial theorem. Do not prove by induction. (1 point) 10b) Prove '() k = n.2n-1 Hint: Take the derivative of both sides of 10a) with respect to x. Now, set x = 1. (2 points) 10c) Prove (*) (7) = n(n+1). 2n-2 k k=1 Hint: Continue with the second derivative of 10a) and proceed as before. The result from 10b) may be useful. (2 points)