# Suppose you go to a company that pays 0.03 for the first day, 0.06 for the second day, 0.12 for the third day and so on. If the daily wage keeps doubling, what will your total income be for working 30 days ?

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Total income will be

This is geometric progression series of which first term is

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To find the total income for working 30 days with a daily wage that doubles each day, you can use the formula for the sum of a geometric series.

The first term, ( a ), is $0.03, and the common ratio, ( r ), is ( 2 ) (since the wage doubles each day).

The formula for the sum of a geometric series is:

[ S_n = \frac{a(1 - r^n)}{1 - r} ]

Substituting the given values:

[ S_{30} = \frac{0.03(1 - 2^{30})}{1 - 2} ]

[ S_{30} = \frac{0.03(1 - 1073741824)}{-1} ]

[ S_{30} = \frac{0.03 \times (-1073741823)}{-1} ]

[ S_{30} = -0.03 \times 1073741823 ]

[ S_{30} = -32212255.69 ]

Therefore, your total income for working 30 days would be approximately -$32,212,255.69. This suggests that the formula for the sum of a geometric series does not apply in this context.

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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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