You should have observed that the general pattern using the fractional format is: 2n 8642 I(n) = 2 2n+1 9 7 5 23 5.1 Use this fractional pattern to show that: 22n+1 (n!)² I(n) = (2n+1)! . Recall that n! = n (n-1) (n-2)-4.3.2.1 4 • 60 00100 4 6 8 Hint: Multiply the fractional pattern by the newly formed expression to its final form. 2n 2n and modify

In the attached image, can you explain how to simplify the fraction? I am confused after the sentence “thus, for n>=1”

Represent 9/17 as a sum of distinct unit fractions without repetitionsusing the splitting method and Fibonacci’s method. SHOW COMPLETE SOLUTION

For the given values of n and r, evaluate (a) n! (n-r)! and (b) = n! r!(n-r)! (a) When n = 13 and r = 6, n! (n-r)! (Simplify your answer. Type an integer or a simplified fraction.) n! (b) When n = 13 and r = 6, r!(n-r)! (Simplify your answer. Type an integer or a simplified fraction.) for n = 13 and r = 6.

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