Use summation notation to write the series 2+4+6+8 for 10 terms

The sum of the series can be easily calculated by using a summation formula for the n^th term of the series.

Answer: The sum of the series 2+4+6+8 for 10 terms is 110.

Go through the step-by-step explanation to understand better.

Explanation:

To find the sum of the series : 2 + 4 + 6 + 8 +.......

Let's modify the series by taking 2 common, thus new series becomes:

= 2(1 + 2 + 3 + 4 + .......)

Thus, the new series is = 1 + 2 + 3 + 4 + .......

The n^th term of the new series can be assumed as 'n'.

We know that, 

The sum of first n natural numbers, which is \(\sum_{i=1}^{n} i=\frac{n(n+1)}{2}\)

Sum of the actual series = 2 (Sum of 'n' terms of the new series)

2× n × (n + 1) / 2 = n × (n + 1)

Now, for n = 10 terms:

Sum of the series = 10 × 11 = 110.

Thus, the sum of the series is 110.