can you help out currently lost need help proving Let us consider parenthesis, as used in a sentence for the written Englishlanguage. The only rule for a single parenthesis is that it must open, we write " (" for that, and itmust close, in which case we write ")".If we use a parenthesis inside another parenthesis, we must make sure that we close the parenthesisinside first, before closing the external parenthesis. Otherwise it is not correctly written. For instance,0) is correct, but )(() is not correct. Let Pn be the number of ways in which n parenthesis can bewritten correctly. The start of the sequence is(Ро, Р, Ра, Рз, ...) %3D (1, 1, 2, 5,...),corresponding to no parenthesis, which gives Po = 1, the unique parenthesis (), which gives P = 1,P2 = 2 because we can write ()) and (()) and finally there are five ways, P3 = 5, of correctly writingMAT 108: PROBLEM SET 33three parenthesis:)00,0(0),(0)0), (O0),((O)).Show that Pn satisfy the following recursionnPn+1 => Pk Pn-k-k=0

Name: can you help out currently lost need help proving Let us consider pare
Uploaded: 2024-03-20T07:07:37.000Z
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Description: can you help out currently lost need help proving Let us consider parenthesis, as used in a sentence for the written Englishlanguage. The only rule for a single parenthesis is that it must open, we write " (" for that, and itmust close, in which case