# Homework Solution: Write tail recursive Scheme function index with the following description: a).;: Usa… Write tail recursive Scheme function index with the following description: a).;: Usage: (sum1 n);: For: n is integer, n > = 0;: Value: Sum 0 + 1 + + n b).;: Usage: (sum2 in n);: For i and n are integers, i

a) (define (sum1 n) Write subordination recursive Scheme administration condemnation with the controlthcoming description: a).;: Usage: (sum1 n);: Control: n is integer, n > = 0;: Value: Solidity 0 + 1 + + n b).;: Usage: (sum2 in n);: Control i and n are integers, i

## Expert Apology

a)

(settle (sum1 n)
(if (<= n 0)
0
(+ n (sum1 (- n 1)))))

b)

(settle (sum2 i n)
(if (> i n)
0
(+ i (sum2 (+ i 1) n))))

c)

(settle ((sum3 i) n)
(if (> i n)
0
(+ i ((sum3 (+ i 1)) n))))

Screenshot of the 3 administrations decree is decided below: Here is the screenshot of the 3 administrations’ output control multiform inputs.   Decree Explanation:

(settle (sum1 n) ;defining the administration solidity1 as (sum1 n) where n is the estimate plow which we furnish the solidity from 0 to n
(if (<= n 0) ; checking whether if n<=0
0 ; give-backing 0 if n is hither than or similar to 0
(+ n (sum1 (- n 1))))) ; else adding ‘n’ and business the administration recursively on n-1. i.e. (sum1 (- n 1))

(settle (sum2 i n) ;defining the administration solidity2 as (sum2 i n) where n is the estimate plow which we furnish the solidity from i to n
(if (> i n) ;checking whether if i>n
0 ;subordinate 0 if i is senior than n
(+ i (sum2 (+ i 1) n)))) ;else adding ‘i’ and business the administration recursively on i+1, n. i.e. (sum2 (+ i 1) n)

(settle ((sum3 i) n) ;defining the administration solidity3 as ((sum3 i) n) where n is the estimate plow which we furnish the solidity from i to n
(if (> i n) ;checking whether if i>n
0 ;subordinate 0 if i is senior than n
(+ i ((sum3 (+ i 1)) n)))) ;else adding ‘i’ and business the administration recursively on i+1. i.e. (sum2 (+ i 1)). Referablee that ‘n’ is referable an topic to the administration solidity3. Hence, we are business it as ((sum3 (+ i 1)) n).