What's the summation of the following series upto infinity 1) 1-1+1-1+1-1+1-1+.…. 2) 1-2+3-4+5-6+7-8+.….….….…. 3) 1+2+3+4+5+6+7+.….….….…….

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Summation of Infinite Series

Series 1: 1-1 1-1 1-1 1-1 ...

This series has no limit as the terms keep alternating between 0 and 1. Therefore, the summation of this series does not exist.

Series 2: 1-2 3-4 5-6 7-8 ...

If we look at each pair of terms in this series, we can see that the sum is always -1. Therefore, we can rewrite the series as:

(-1) + (-1) + (-1) + (-1) + ...

This is an infinite series of -1s, which does not converge. Therefore, the summation of this series does not exist.

Series 3: 1 2 3 4 5 6 7 ...

This is an infinite series of consecutive positive integers. We can find the sum of this series using the formula:

Sum = n(n+1)/2

where n is the last term in the series. In this case, n is infinity, so the sum is:

Sum = infinity * (infinity + 1) / 2

This expression is undefined as infinity is not a number. Therefore, the summation of this series does not exist.

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Actual answers are1) 1/2  2)1/4  3)-1/12

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1)1/2 2)1/4 3)-1/12

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How to solve it

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Infinite

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Show me answer of this question

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1) 1/2. 3)-1/12 2)i dont know

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1)0..2)infinity... 3)infinity