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2 years ago

Please answer with steps

Mathematics

1 answer:

egoroff_w [7]2 years ago

7 0

9514 1404 393

Answer:

n = 99

Step-by-step explanation:

The sum of logarithms is the log of a product. Here, the sum of terms is ...

log(2/1) +log(3/2) +log(4/3) + ... +log((n+1)/n)

= log((2/1)(3/2)(4/3)×...×((n+1)/n)) = log(n+1)

So, the question reduces to ...

log(n+1) = 2

Taking antilogs, we have ...

n +1 = 10^2 = 100

n = 99

The value of n that makes the sum 2 is 99.

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