Use mathematical induction to prove that the statement is true for every positive integer n. 1...
Question:
Use mathematical induction to prove that the statement is true for every positive integer n.
{eq}1 . 4 + 2 . 4 + 3 . 4 + . . . + 4n = 4n(n+1)/2 {/eq}
Induction:
Mathematical induction is a proof technique wherein given a true statement {eq}P(k) {/eq} for every {eq}k\in\{1,2,3,\ldots, n\} {/eq} we show that {eq}P(n+1) {/eq} is also true.
This inductive reasoning implies that the statement is true for all natural numbers {eq}\{1,2,3,\ldots\} {/eq}
Answer and Explanation: 1
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View this answerFor {eq}n=1 {/eq} we have
$$\begin{align} 1\cdot 4 &= 4 \\[8pt] &= \frac{4(1)(2)}{2} \end{align} $$ and the equation holds.
Suppose for all...
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Proving Divisibility: Mathematical Induction & Examples
from
Chapter 2 / Lesson 3
405
Mathematical induction is the process of showing that all cases in a series are true if one particular case is true. Learn how to apply mathematical induction to prove divisibility and practice the method by working examples.
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