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The sum of the series log b to the base a log b^2 to the base a^2 log b^3 to the base a^3 . log b^n to the base a^n is given by a) log b^n to the base a b) log b to the base a^n c) log b^n to the base a^n d) None?
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The sum of the series log b to the base a log b^2 to the base a^2 ...
Sum of the Series:
The given series is:
log b to the base a + log b^2 to the base a^2 + log b^3 to the base a^3 + ... + log b^n to the base a^n

Simplifying the Series:
We can simplify the given series using the logarithmic property log a^b to the base c = b * log a to the base c.

Using this property, we can rewrite each term in the series as follows:
log b to the base a = 1 * log b to the base b = log b to the base b = 1
log b^2 to the base a^2 = 2 * log b to the base b = 2
log b^3 to the base a^3 = 3 * log b to the base b = 3
...
log b^n to the base a^n = n * log b to the base b = n

So, the simplified series becomes:
1 + 2 + 3 + ... + n

Sum of the Series:
The sum of the series 1 + 2 + 3 + ... + n is given by the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is:
Sum = (n/2) * (first term + last term)

In this case, the first term is 1 and the last term is n. So, substituting these values into the formula, we get:
Sum = (n/2) * (1 + n)

Therefore, the sum of the given series log b to the base a + log b^2 to the base a^2 + log b^3 to the base a^3 + ... + log b^n to the base a^n is:
(n/2) * (1 + n)

Answer:
The sum of the series log b to the base a + log b^2 to the base a^2 + log b^3 to the base a^3 + ... + log b^n to the base a^n is given by option c) log b^n to the base a^n, which is (n/2) * (1 + n).
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The sum of the series log b to the base a log b^2 to the base a^2 log b^3 to the base a^3 . log b^n to the base a^n is given by a) log b^n to the base a b) log b to the base a^n c) log b^n to the base a^n d) None?
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The sum of the series log b to the base a log b^2 to the base a^2 log b^3 to the base a^3 . log b^n to the base a^n is given by a) log b^n to the base a b) log b to the base a^n c) log b^n to the base a^n d) None? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of the series log b to the base a log b^2 to the base a^2 log b^3 to the base a^3 . log b^n to the base a^n is given by a) log b^n to the base a b) log b to the base a^n c) log b^n to the base a^n d) None? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series log b to the base a log b^2 to the base a^2 log b^3 to the base a^3 . log b^n to the base a^n is given by a) log b^n to the base a b) log b to the base a^n c) log b^n to the base a^n d) None?.
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