Question

.3 3. True or False? For any integer m, 2m(3m + 2) is divisible by 4. Explain to get credit.

Answer 1

Answer with explanation:

We have to prove that, For any integer m, 2 m×(3 m + 2) is divisible by 4.

We will prove this result with the help of Mathematical Induction.

⇒For Positive Integers

For, m=1

L HS=2×1×(3×1+2)

      =2×(5)

       =10

It is not divisible by 4.

⇒For Negative Integers

For, m= -1

L HS=2×(-1)×[3×(-1)+2]

      =-2×(-3+2)

       = (-2)× (-1)

       =2

It is not divisible by 4.

False Statement.