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Step-by-step Answer
PAGE: 625SET: ExercisesPROBLEM: 1
Please look in your text book for this problem Statement

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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