Question

What is the value of (-1)×(-1)×.... 10 times

Answer 1

Answer:

1

Step-by-step explanation:

Let's see the proof of one simple theorem using induction method.

Thereom => (-1)^n = 1 , if n is even.

= -1 , if n is odd.

As we know, -1 × -1 = 1

So, if n = 2, the thereom is correct.

Also, for n = 1, -1 = -1, thereom is true.

Assume, the thereom is true for k.

Let's see for n = k+1.

If k is even, (-1)^k = 1, and n becomes odd.

(-1)^ n = (-1)^(k+1) = (-1)^k × (-1)^1 = 1 × (-1) = -1

Which is true, as for n = odd, the value is -1.

Similarly, if k is odd, (-1)^k = -1, and n becomes even.

(-1)^ n = (-1)^(k+1) = (-1)^k × (-1)^1 = (-1) × (-1) = 1

Which is true, as for n = even, the value is 1.

From induction, the above thereom is true.

For given question, use the above thereom.

For n = 10, which is even,

(-1)^10 = 1

Hope it may help you.