Solve :
$501 imes 502$

Q: Solve : $501\times 502$

To solve the problem $501 \times 502$, we can use the algebraic identity for the product of two consecutive numbers, which is: \[ n \times (n+1) = n^2 + n \] In this case, $n = 501$. Therefore, we calculate: \[ 501 \times 502 = 501^2 + 501 \] First, we calculate $501^2$: \[ 501^2 = (500 + 1)^2 = 500^2 + 2 \times 500 \times 1 + 1^2 \] Calculating each term separately: \[ 500^2 = 250000 \] \[ 2 \times 500 \times 1 = 1000 \] \[ 1^2 = 1 \] Adding these together: \[ 501^2 = 250000 + 1000 + 1 = 251001 \] Now, add 501 to this result: \[ 501 \times 502 = 251001 + 501 = 251502 \] Thus, the correct answer is indeed Option 3: 251502. **Explanation for Incorrect Options:** 1. **Option 1: 152502** - This result is incorrect because it does not match the calculated product of $501 \times 502$. The calculation shows that the correct product is 251502, not 152502. 2. **Option 2: 125502** - This option is incorrect for the same reason as Option 1. The calculated product is 251502, which is significantly different from 125502. 3. **Option 4: 551202** - This option is also incorrect. The calculated product is 251502, and 551202 is much larger than the correct result. In conclusion, the correct answer is Option 3: 251502, as demonstrated by the detailed calculation using the algebraic identity for the product of consecutive numbers.

Question

Solve : 
$501	imes 502$

Accepted Answer

To solve the problem $501 \times 502$, we can use the algebraic identity for the product of two consecutive numbers, which is:

$$
n \times (n+1) = n^2 + n
$$

In this case, $n = 501$. Therefore, we calculate:

$$
501 \times 502 = 501^2 + 501
$$

First, we calculate $501^2$:

$$
501^2 = (500 + 1)^2 = 500^2 + 2 \times 500 \times 1 + 1^2
$$

Calculating each term separately:

$$
500^2 = 250000
$$
$$
2 \times 500 \times 1 = 1000
$$
$$
1^2 = 1
$$

Adding these together:

$$
501^2 = 250000 + 1000 + 1 = 251001
$$

Now, add 501 to this result:

$$
501 \times 502 = 251001 + 501 = 251502
$$

Thus, the correct answer is indeed Option 3: 251502.

**Explanation for Incorrect Options:**

1. **Option 1: 152502** - This result is incorrect because it does not match the calculated product of $501 \times 502$. The calculation shows that the correct product is 251502, not 152502.

2. **Option 2: 125502** - This option is incorrect for the same reason as Option 1. The calculated product is 251502, which is significantly different from 125502.

3. **Option 4: 551202** - This option is also incorrect. The calculated product is 251502, and 551202 is much larger than the correct result.

In conclusion, the correct answer is Option 3: 251502, as demonstrated by the detailed calculation using the algebraic identity for the product of consecutive numbers.