Algebra 2, 2008

 PAGE: 672 SET: Exercises PROBLEM: 2

The given equation is .

When n = 1,

Left side of the given equation is .

Right side is .

Thus, the equation is true for .

Assume for a positive integer k.

Show that the given equation is true for .

(The LCM of is )

(Apply standard division form: )

(Cancel common term)

The last expression is the right side of the equation to be proved.

When n is replaced by k + 1.

Therefore the equation is true for n = k + 1.

The equation is true for all values of n.

The given statement is true for any positive integer.

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