SOLUTION: Show that the terms of the series ∑n r=1 log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms

Question 1198089: Show that the terms of the series ∑n r=1 log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms exceeds 400.[ans: S20 = 146.78, n = 34]
Found 3 solutions by greenestamps, math_tutor2020, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

It is not at all clear from your post what the sequence is. It looks like

With any interpretation I can see for the sequence, we always end up with a logarithmic sequence; but no such sequence is an AP, so the problem doesn't make sense.

Re-post, making the question clear.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Use the rule that log(A*B) = log(A)+log(B)

See note1 below

See note2 below

which is approximate

It seems strange that your teacher is getting , so I have a feeling I might be mis-interpreting the given expression.

Footnotes:
note1: The first parenthesis grouping has 20 copies of "log(5)" added together, which leads to 20*log(5) in the next line.
note2: Use the rule log(A)+log(B) = log(A*B). The log(1*2*3*...*20) leads to log(20!) where the exclamation mark indicates factorial.

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

                    To the next generation of students, who will read this post.

Simply ignore it and do not waste your time, since the post is mathematically unreadable,
mathematically incorrect and mathematically non-sensical.

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