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There are fifty successive percentage discounts given in a series of 2%, 4%, 6%, 8%... and so on. What is the net discount?

  • a)
    98%

  • b)
    2550%

  • c)
    100%

  • d)
    Infinite

Correct answer is option 'C'. Can you explain this answer?
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There are fifty successive percentage discounts given in a series of 2...
Given: A series of fifty successive percentage discounts in the form of 2%, 4%, 6%, 8%, and so on.

To find: The net discount.

Solution:

We can first find the sum of the series to get the total percentage discount.

The series is an arithmetic progression with a common difference of 2.

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

Sum = n/2[2a + (n-1)d]

Where n = 50 (number of terms), a = 2 (first term), and d = 2 (common difference).

Substituting these values, we get:

Sum = 50/2[2(2) + (50-1)(2)] = 50/2[4 + 98] = 50/2(102) = 2550

Therefore, the total percentage discount is 2550%.

To find the net discount, we need to find the equivalent single discount that will give the same overall discount as the series of discounts.

We can use the formula:

Net discount = 100 x [(100 - D1) x (100 - D2) x ... x (100 - Dn)]/100^n

Where D1, D2, ..., Dn are the individual discounts.

Substituting the values of D1, D2, ..., Dn as 2%, 4%, 6%, 8%, and so on, we get:

Net discount = 100 x [(100 - 2) x (100 - 4) x ... x (100 - 100)]/100^50

Simplifying this expression, we get:

Net discount = 100 x 98/100^50 = 100 x 2^-49

This value is very close to zero and can be considered as negligible.

Therefore, the net discount is approximately 100%.

Hence, the correct option is (c) 100%.
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There are fifty successive percentage discounts given in a series of 2%, 4%, 6%, 8%... and so on. What is the net discount?a)98%b)2550%c)100%d)InfiniteCorrect answer is option 'C'. Can you explain this answer?
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