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Abstract Mathematics | Fall 2009 | Shubleka
Name _______________________
⎡ ( −1)i ⎤ 1. Prove: for every odd integer n ≥ 3 , ∏ ⎢1 + ⎥ = 1 , where Π is the generalized product, just i ⎦⎥ i =2 ⎢ ⎣ like Σ is the generalized sum. 2. Prove: for every integer n ≥ 4, 2n < n !. n
3. Prove: for all positive integers n ≥ 2,
n
∑ i =1
1 > n. i
Name _______________________
⎡ ( −1)i ⎤ 1. Prove: for every odd integer n ≥ 3 , ∏ ⎢1 + ⎥ = 1 , where Π is the generalized product, just i ⎦⎥ i =2 ⎢ ⎣ like Σ is the generalized sum. 2. Prove: for every integer n ≥ 4, 2n < n !. n
3. Prove: for all positive integers n ≥ 2,
n
∑ i =1
1 > n. i
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