Reference no: EM13960625
1) Use mathematical proofs to show that:
1 + 3 + 5 + . . . + (2n - 1) = n^2 (^2 means n to the power of 2)
2) Let n and k be some integers with 0 <= k <= n. Then, what is the binomial coefficient formula expression in terms of n and k?
3) Explain and provide proofs for the following:
4) For every positive integer n,
Let P(n) be the formula: 12 + 22 + ... + n2 = (n (n+1)(2n + 1)) / 6
a. What is the value of P(1)? Is P(1) true?
b. What is the value of P(10)? Is P(10) true?
c. What is the value of P(k), the value of P(k+1)?
5) Please provide a counterexample to disprove each of the following:
a. For all real numbers a and b, if a2 = b2 then a = b
b. For all real numbers a and b, if a3 = b3 then a = b
c. For all integers m and n, if 2m + n is odd then m and n are odd
d. For all integers m and n, if 2m - n is even then m and n are even.
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Describes the government or nonprofit organization
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: What is the value of P(10)? Is P(10) true? Let n and k be some integers with 0
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