The average of all the non negative integers upto 99 is:

Options

A. 50.49
B. 49.5
C. 50.5
D. 99

Answer

To find the average of all non-negative integers up to 99, we can follow these steps:

### Step 1: Identify the range of integers
The non-negative integers up to 99 are the integers from 0 to 99. This means we have the numbers: 0, 1, 2, ..., 99.

### Step 2: Calculate the number of integers
The total count of integers from 0 to 99 is:
\[ 99 - 0 + 1 = 100 \]
So, there are 100 integers.

### Step 3: Calculate the sum of the integers
To find the sum of all integers from 0 to 99, we can use the formula for the sum of the first n integers, which is:
\[ S = \frac{n(n + 1)}{2} \]
In our case, n is 99. Therefore, the sum is:
\[ S = \frac{99 \times (99 + 1)}{2} = \frac{99 \times 100}{2} \]
Calculating this gives:
\[ S = \frac{9900}{2} = 4950 \]

### Step 4: Calculate the average
The average is calculated by dividing the sum by the number of integers:
\[ \text{Average} = \frac{\text{Sum}}{\text{Count}} = \frac{4950}{100} \]
Calculating this gives:
\[ \text{Average} = 49.5 \]

### Final Answer
The average of all non-negative integers up to 99 is **49.5**.

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