Question

For some integer m, every even integer is the form of:

Answer 1

Answer:

2m

Step-by-step explanation:

We know that an integer is said to be even when it

is divisible by 2.

Let m be a integer i.e. m = ..., -3, -2, -1, 0, 1, 2, 3, ..

Clearly, 'm' may or may not be even, therefore, 'm'

can't be an answer.m + 1 = ..., -2, -1, 0, 1, 2, 3,

4...Here also, 'm + 1' may or may not be even,

therefore, 'm + 1' can't be an answer.

Now, consider 2m i.e. 2m = ...,-6, -4, -2, 0, 2, 4, 6,...

Here, for some integer m, 2m is always integer,

Now, consider 2m + 1, i.e. 2m + 1 = ..., -5, -3, -1, 1, 3,

5, 7,.Clearly, 2m + 1 is an odd integer, therefore it

can't be an answer.

Hence, 2m is only answer.