In $(2\times n) -1$, if you substitute any whole number greater than 0 for n will you get an even or odd number ? Why ? What about $(2\times n) +1$

Given :

The given terms are $(2\times n) -1$ and $(2\times n) +1$.

To do :

We have to find for any whole number greater than 0, the value of the given terms will be odd or even.

Solution :

 $(2\times n) -1$

For any $n>0$

If $n = 1$

$(2\times1)-1 = 2-1 = 1$

If $n=2$

$(2\times2)-1 = 4-1 = 3$

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.

.

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This implies,

For any $n>0, (2\times n)-1$ is an odd number.

$(2\times n) +1$

For any $n>0$

If $n = 1$

$(2\times1)+1 = 2+1 = 3$

If $n=2$

$(2\times2)+1 = 4+1 = 5$

.

.

.

.

This implies,

For any $n>0, (2\times n)+1$ is an odd number.

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Updated on: 10-Oct-2022

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