212k views
4 votes
Let a_i = 1, 2, 3, ..., i for i = 1, 2, 3, .... Find

1 Answer

2 votes

Final answer:

The sum of the series defined by a_i = 1, 2, 3, ..., i for i = 1, 2, 3, .... is undefined.

Step-by-step explanation:

The given question is asking us to find the value of a series defined by the sequence of numbers a_i = 1, 2, 3, ..., i for i = 1, 2, 3, ....

So, the series can be written as: 1, 2, 3, 4, 5, 6, ...

This is an arithmetic sequence with a common difference of 1. To find the value of the series, we can use the formula for the sum of an arithmetic series:

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

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

In this case, a = 1 and the series continues indefinitely, so we can use the formula for the sum of an infinite arithmetic series:

S = (a/1 - r)

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

Substituting the values into the formula, we get:

S = (1/1 - 1)

S = (1/0)

Since division by 0 is undefined, the sum of this series is undefined.

User Bryan Goggin
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories