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| PAGE: 625 | SET: Exercises | PROBLEM: 1 |
The conjecture is 
.
Let 
be the statement that .
Verify that is true for 
.
Substitute in .
is true for 
.
Assume that is true for 
.
Substitute in .
.
is true for positive integer 
.
Show that 
must be true.
Add 
to each side.
.
The final statement is exactly , so is true.
Because is true for and implies , is true for 
and so on.
That is, by the principle of mathematical induction,
is true for all positive integers 
.
By the principle of mathematical induction, is true for all positive integers .
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