Description
Solve all the 6 exercises on the worksheet on your own paper or by using your favorite software.
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𝑛
∑ (2𝑖 − 1) = 𝑛2
𝑖=1
𝑛
𝑖
𝑛
∑ (−1) 𝑖2 = (−1)
𝑖=1
𝑛
∑
1
2
𝑖=1 𝑖
𝑛(𝑛+1)
2
< 2 − 1𝑛
𝑛
∑ 𝑖 ⋅ (𝑖!) = (𝑛 + 1)! − 1whenever𝑛 ∈ ℤ+ .
𝑖=1
𝑛 + 1 ≤ 2𝑛
1 ≤ 2𝑛 .
𝑎
(1 + 𝑎)𝑛 ≥ 1 + 𝑛𝑎
𝑎 > −1
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Tags:
discrete mathematics
Mathematical induction
positive integers
inductivestep
basis step
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