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oksano4ka [1.4K]
2 years ago
9

Prove the statement by mathematical induction.

Mathematics
2 answers:
olganol [36]2 years ago
7 0
69 is the correct answer
Lyrx [107]2 years ago
3 0

Answer:

3 + 5 + 7 + . . . + (2n + 1) = n(n + 2)  ,for n ≥ 1

Step-by-step explanation:

3 + 5 + 7 + . . . + (2n + 1) = n(n + 2)

1. proposition is true when n = 1,

since n(n + 2) = (1 + 2) = 3 = 2(1) + 1 = 3 + 5 + 7 + . . . + (2n + 1)

2. We will assume that the proposition is true for a constant k = n

so, 3 + 5 + 7 + . . . + (2k + 1) = k(k + 2)

3. Then, 3 + 5 + 7 + . . . + (2k + 1) + (2k + 3) = k(k + 2) + (2k +3 ) = (k + 1)(k + 3)

<u>Conclusion</u> :

According to the Principle of Mathematical Induction :

3 + 5 + 7 + . . . + (2n + 1) = n(n + 2)  ,for n ≥ 1

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