Show by induction that 1+3 +5+ . + (2n – 1) = n² ...

Use induction to show that 12 -7 is divisible by 5.

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. 16) 4 + 9 + 14 + .+ (5n - 1) = (5n + 3) 16). %3D

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Click and drag the steps in the correct order to show that 6 divides n³- n whenever n is a nonnegative integer using mathematical induction. BASIS STEP: INDUCTIVE STEP: 6 (131), i.e., 610, the basis step is true. 61 (03-0), i.e., 6 1 0, so the basis step is true. Suppose that 6 | k³ - k. By the inductive hypothesis, 61 (k³k). Clearly, 31 3k(k+1), but 3k(k+ 1) is also even as one of kor k+ 1 is even; therefore, 6 | 3k(k+ 1) as well. By the inductive hypothesis, 3 I (K³-k). Clearly, 31 3k(k+1), but 3k(k+ 1) is also odd as one of k or k + 1 is even; therefore, 6 | 3k(k+ 1) as well. (k+ 1)³(k+ 1) = (k³ + 3k² + 3k + 1) − (k+ 1) = (k³ k) + 3k(k+1) As the sum of two multiples of 6 is again divisible by 6, 61 ((k+ 1)³ − (k+ 1)).

This is a practice question from my Discrete Mathematical Structures Course. Thank you.

Discrete Math Use induction to show that n^4 + 15 is a multiple of 16 for every positive odd integer n.

Use the principle of mathematical induction to prove that 1 +r+r² +r³ + ... + pn = pn+1 - r-1