* Question Completion Status: Show the following relationship holds for all positive integers: 2 + 4 + . + 2n = n(n + 1) Step 1: Show true for n = 1 TRUE -1(1+1) Step 2: Assume true for an arbitrary integer n = k Step 3: Show true for the next element of the domain. That is, show that From the Induction Hypothesis: 2 + 4 + ... + 2k= k(k + 1) Since this is an equation: 2 + 4 + ... + 2k + 2(k+ 1) = k(k + 1) + 2 +4 + ... + 2k +2(k+1) = k² + k + 2(k+ 1) 2 + 4 + ... + 2k +2(k+1) = Step 4: Therefore, by the Principle of Mathematical Induction for all positive integers: 2 + 4 + ... + 2n = n(n + 1) .

* Question Completion Status: Show the following relationship holds for all positive integers: 2 + 4 + . + 2n = n(n + 1) Step 1: Show true for n = 1 TRUE -1(1+1) Step 2: Assume true for an arbitrary integer n = k Step 3: Show true for the next element of the domain. That is, show that From the Induction Hypothesis: 2 + 4 + ... + 2k= k(k + 1) Since this is an equation: 2 + 4 + ... + 2k + 2(k+ 1) = k(k + 1) + 2 +4 + ... + 2k +2(k+1) = k² + k + 2(k+ 1) 2 + 4 + ... + 2k +2(k+1) = Step 4: Therefore, by the Principle of Mathematical Induction for all positive integers: 2 + 4 + ... + 2n = n(n + 1) .

Name: Please please help me soving this question completely Question Complet
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please please help me soving this question completely Question Completion Status:Show the following relationship holds for all positive integers: 2 + 4 + ... + 2n = n(n + 1)Step 1: Show true for n = 1TRUE-1(1+1)Step 2: Assume true for an arbitrary in