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| 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 
.
(Add 
to each side)
(The LCM of 
is 
)
(Add: 
)
(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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