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.
