#26 Proof Principle of Mathematical Induction 2+4+6+ 2n nn+1 mathgotserved induction worksheet exa - Free Printable

Educational worksheet: #26 Proof Principle of Mathematical Induction 2+4+6+ 2n nn+1 mathgotserved induction worksheet exa. Download and print for classroom or home learning activities.

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1. Base Case (n = 1):
Left-hand side: 2(1) = 2.
Right-hand side: 1(1 + 1) = 2.
Since both sides are equal, the statement holds for n = 1.

2. Inductive Hypothesis:
Assume the statement is true for some positive integer k:
2 + 4 + 6 + ... + 2k = k(k + 1).

3. Inductive Step (Prove for n = k + 1):
Consider the sum up to 2(k + 1):
2 + 4 + 6 + ... + 2k + 2(k + 1).
By the inductive hypothesis, this equals:
k(k + 1) + 2(k + 1).
Factor out (k + 1):
(k + 1)(k + 2).
This is equal to (k + 1)((k + 1) + 1), which matches the right-hand side for n = k + 1.

4. Conclusion:
By mathematical induction, the statement 2 + 4 + 6 + ... + 2n = n(n + 1) is true for all positive integers n.

Parent Tip: Review the logic above to help your child master the concept of mathematical induction worksheet.

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