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CBSE Class 9 Mathematics Question 9 of 17

Proofs in Mathematics — Question 4

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4
Question

Question 4

Look at the following pattern :

12 = 1

112 = 121

1112 = 12321

11112 = 1234321

111112 = 123454321

Make a conjecture about each of the following:

1111112 =

11111112 =

Check if your conjecture is true.

Answer

Looking at above pattern,

Possible conjecture :

The resultant will be series of numbers from one till number of 1's in the digit to be squared and then reversing the order.

By following conjecture, we can write:

⇒ 1111112 = 12345654321 and

⇒ 11111112 = 1234567654321

On actual multiplication, we get :

⇒ 1111112 = 12345654321 and

⇒ 11111112 = 1234567654321.

Hence, conjecture is true.