# How do you find the sum of the infinite series #Sigma(1/10)^k# from k=1 to #oo#?

Find the common ratio, by calculating the first three terms.

Ratio:

This could have been seen from the summation expression.

The sum of a geometric series is:

So:

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To find the sum of the infinite series Σ(1/10)^k from k=1 to ∞, you can use the formula for the sum of an infinite geometric series, which is given by S = a / (1 - r), where "a" is the first term and "r" is the common ratio. In this series, the first term "a" is 1/10 and the common ratio "r" is also 1/10. So, plugging these values into the formula, you get:

S = (1/10) / (1 - 1/10)

Simplify the expression:

S = (1/10) / (9/10) S = (1/10) * (10/9) S = 1/9

Therefore, the sum of the infinite series Σ(1/10)^k from k=1 to ∞ is 1/9.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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