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The sum of a series of numbers can be derived using the formula for the sum of an arithmetic series or the sum of a geometric series.

1. Sum of an arithmetic series:

The sum of an arithmetic series can be found using the formula:

S = (n/2)(a + l)

where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

2. Sum of a geometric series:

The sum of a geometric series can be found using the formula:

S = a(1 - r^n) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

These formulas can be derived using mathematical induction or other methods, but they are widely accepted and used to find the sum of series in mathematics.

1. Sum of an arithmetic series:

The sum of an arithmetic series can be found using the formula:

S = (n/2)(a + l)

where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

2. Sum of a geometric series:

The sum of a geometric series can be found using the formula:

S = a(1 - r^n) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

These formulas can be derived using mathematical induction or other methods, but they are widely accepted and used to find the sum of series in mathematics.

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