Question

Find the sum: 0 + – 4 + – 8 + ... + (4 – 4n)

a) n(2n + 1)
b) n(2n – 1)
c) n(2n + 2)
d) n(2n – 2)

Answer 1

To find the sum of the given series, use the formula for the sum of an arithmetic series and simplify the expression to get the sum as n(2n - 1).

Step-by-step explanation:

To find the sum of the given series 0 + – 4 + – 8 + ... + (4 – 4n), we can observe that each term is obtained by subtracting 4 from the previous term. So, the common difference is -4. We can write the nth term as (4 - 4n). To find the sum of the series, we can use the formula for the sum of an arithmetic series:

S = (n/2)(first term + last term)

Substituting the values, the sum of the series is S = (n/2)(0 + (4 - 4n)). Simplifying the expression, we get S = (n/2)(4 - 4n), which is equivalent to option (b) n(2n - 1).