Practice Variable as Generalization in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A variable standing for any arbitrary member of a specified set, used to express statements that hold universally.
'For any number n, n + 0 = n' works for ALL numbers, not just one.
Example 1
easyShow that a + b = b + a holds for a = 5, b = 3 and for a = -2, b = 7.
Example 2
mediumExplain why (n+1)^2 - n^2 = 2n + 1 is true for every integer n.
Example 3
easyIs x \cdot 0 = 0 a generalization or an equation to solve?
Example 4
mediumWrite a general formula for the sum of the first n positive integers.