Math Snap

STEP 1

Assumptions1. The series O represents the sum of odd numbers from3 to103.
. The series represents the sum of even numbers from4 to104.
3. Both series are arithmetic series, with a common difference of.

STEP 2

First, we need to find the number of terms in each series. The formula to find the number of terms in an arithmetic series is$$n = \frac{Last\, term - First\, term}{Common\, difference} +1$$

STEP 3

Calculate the number of terms in series O.
$$n = \frac{103 -3}{2} +1$$

STEP 4

Calculate the number of terms in series.
$$n_E = \frac{104 -4}{2} +1$$

STEP 5

The sum of an arithmetic series can be found using the formula$$Sum = \frac{n}{2} \times (First\, term + Last\, term)$$

STEP 6

Calculate the sum of series O without actually computing the sum.
$$= \frac{n}{2} \times (3 +103)$$

STEP 7

Calculate the sum of series without actually computing the sum.
$$= \frac{n_E}{2} \times (4 +104)$$

STEP 8

Now, we need to find which series has a greater sum and by how much. We can do this by subtracting the smaller sum from the larger sum.
If $>$, then $Difference = O -$
If $> O$, then $Difference = - O$

Finally, simplify the difference to find which series has a greater sum and by how much.