If A = log 1 + log 2 + log 3 + .......... log n and B = log ((n - 1)!), which of the following must be true? n is a natural number.

- a)A > B
- b)A < B
- c)A = B
- d)A
__>__B - e)A
__<__B

Correct answer is option 'D'. Can you explain this answer?

Related Test: NMAT Mock Test - 4

3 Answers

Krishna
answered
Apr 02, 2020

A = log 1 + log 2 + log 3 + ..........+ log n = log (1 * 2 * 3 x 4 x ... x n) = log(n!)

B = log ((n - 1)!)

Since n is a natural number,

for any n > 1, A > B

For n = 1, A = log (1!) = log 1 and B = log (0!) = log 1

i.e. A = B

Thus, A > B

Hence, option 4.

B = log ((n - 1)!)

Since n is a natural number,

for any n > 1, A > B

For n = 1, A = log (1!) = log 1 and B = log (0!) = log 1

i.e. A = B

Thus, A > B

Hence, option 4.

Akash Singh
answered
Mar 04, 2020

Log xy = log x + log y

A = log1 + log 2 .... + log n

A = log(1.2.3....n)

A = log(n!)

A = log(n.(n-1)!)

A = log n + log ((n-1)!)

A = log n + B

Since log n >= 0

A >= B

A = log1 + log 2 .... + log n

A = log(1.2.3....n)

A = log(n!)

A = log(n.(n-1)!)

A = log n + log ((n-1)!)

A = log n + B

Since log n >= 0

A >= B

This discussion on If A = log 1 + log 2 + log 3 + ..........log n and B = log ((n- 1)!), which of the following must be true? n isa natural number.a)A Bb)A Bc)A = Bd)A Be)A BCorrect answer is option 'D'. Can you explain this answer? is done on EduRev Study Group by CAT Students. The Questions and
Answers of If A = log 1 + log 2 + log 3 + ..........log n and B = log ((n- 1)!), which of the following must be true? n isa natural number.a)A Bb)A Bc)A = Bd)A Be)A BCorrect answer is option 'D'. Can you explain this answer? are solved by group of students and teacher of CAT, which is also the largest student
community of CAT. If the answer is not available please wait for a while and a community member will probably answer this
soon. You can study other questions, MCQs, videos and tests for CAT on EduRev and even discuss your questions like
If A = log 1 + log 2 + log 3 + ..........log n and B = log ((n- 1)!), which of the following must be true? n isa natural number.a)A Bb)A Bc)A = Bd)A Be)A BCorrect answer is option 'D'. Can you explain this answer? over here on EduRev! Apart from being the largest CAT community, EduRev has the largest solved
Question bank for CAT.

Ask a question

- Plz explain
Doc | 1 Page

- Building Line Following and Food Following Robots
Doc | 19 Pages

- Short Answer Questions - Natural Vegetation and Wildlife
Doc | 11 Pages

Upgrade to Infinity