Question

Find the sum of n terms of the series (4(1)/(n))+(4(2)/(n))+(4(3)/(n))+dotsdots

Answer 1

To find the sum of n terms of the given series, simplify the series and use the formula for the sum of an arithmetic series.

Step-by-step explanation:

The given series is

(4(1)/n)+(4(2)/n)+(4(3)/n)+...

To find the sum of n terms of the series, we can simplify the series and use the formula for the sum of an arithmetic series.

First, we can rewrite the series as 4[1/n + 2/n + 3/n + ... + n/n].

Next, we can simplify the expression inside the brackets to (1 + 2 + 3 + ... + n)/n.

Using the formula for the sum of an arithmetic series, the sum of the series is (n(n + 1)/2)/n = (n + 1)/2.