Consider a function tetrahedral( ) that computes the n^th tetrahedral number for a given integer n>=0: T(n)= Tri(1)+Tri(2)+Tri(3)+...+Tri(n-1)+Tri(n)    where Tri(n) is defined as Tri(n)+1+2+3+...+(n-1)+n a) Implement the function tetrahedral( ) using recursion in order to perform the repeated additions. b) Find an algebraic representation for T(n) that does not require any repeated additions. Implement the function tetrahedral( ) with a one-line definition using this formula.

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Consider a function tetrahedral( ) that computes the n^th tetrahedral number for a given integer n>=0:

T(n)= Tri(1)+Tri(2)+Tri(3)+...+Tri(n-1)+Tri(n)    where Tri(n) is defined as

Tri(n)+1+2+3+...+(n-1)+n

a) Implement the function tetrahedral( ) using recursion in order to perform the repeated additions.

b) Find an algebraic representation for T(n) that does not require any repeated additions. Implement the function tetrahedral( ) with a one-line definition using this formula.

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