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

Algebra ->  Sequences-and-series -> 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       Log On


   

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) About Me  (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 sum%28log%28%285r%29%29%2C1%2Cn%29

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) About Me  (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



sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+32.365524703598 which is approximate

It seems strange that your teacher is getting S%5B20%5D+=+146.78, 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) About Me  (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.