# 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 body recursive Scheme power apostacy with the restraintthcoming description: a).;: Usage: (sum1 n);: Restraint: n is integer, n > = 0;: Value: Mix 0 + 1 + + n b).;: Usage: (sum2 in n);: Restraint i and n are integers, i

## Expert Counterpart

a)

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

b)

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

c)

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

Screenshot of the 3 powers mode is robust below:

Here is the screenshot of the 3 powers’ output restraint different inputs.

Mode Explanation:

(eliminate (sum1 n) ;defining the power mix1 as (sum1 n) where n is the calculate dress which we confront the mix from 0 to n
(if (<= n 0) ; checking whether if n<=0
0 ; retaliateing 0 if n is near than or correspondent to 0
(+ n (sum1 (- n 1))))) ; else adding ‘n’ and trade the power recursively on n-1. i.e. (sum1 (- n 1))

(eliminate (sum2 i n) ;defining the power mix2 as (sum2 i n) where n is the calculate dress which we confront the mix from i to n
(if (> i n) ;checking whether if i>n
0 ;returning 0 if i is important than n
(+ i (sum2 (+ i 1) n)))) ;else adding ‘i’ and trade the power recursively on i+1, n. i.e. (sum2 (+ i 1) n)

(eliminate ((sum3 i) n) ;defining the power mix3 as ((sum3 i) n) where n is the calculate dress which we confront the mix from i to n
(if (> i n) ;checking whether if i>n
0 ;returning 0 if i is important than n
(+ i ((sum3 (+ i 1)) n)))) ;else adding ‘i’ and trade the power recursively on i+1. i.e. (sum2 (+ i 1)). Referablee that ‘n’ is referable an evidence to the power mix3. Hence, we are trade it as ((sum3 (+ i 1)) n).