Can you please help me with this problem because I am really struggling with this and the parts with it. Can you please label the parts and can you do it step by step so I can follow along and see how you did it 30.11 Let S (n) = 1 + 2 + + n be the sum of the first n natural numbers and letC(n) = 1³ +23³ +...+n³ be the sum of the first n cubes. Prove the followingequalities by induction on n, to arrive at the curious conclusion that C(n) = S² (n)3forevery n.a. S(n) =b. C(n) =n(n + 1).(n + 2n³ + n²) = n² (n + 1)².

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Let S(n) = 1 + 2 + + n be the sum of the first n natural numbers and let C(n) = 1³+2³+. + n³ be the sum of the first n cubes. Prove the following equalities by induction on n, to arrive at the curious conclusion that C(n) = S² (n) for every n. ... a. S(n) = n(n+1). b. C(n)=(n + 2n³ + n²) = n²(n + 1)².