Maths-
General
Easy
Question
- log 12
- log 11
Hint:
In this question, we have given 
. We have to find the sum of this series, for that open the bracket and find the sum.
The correct answer is:
Here we have to find the sum of the series.
Firstly, the given series is
S = 
…..
We can write
S = 
We know that,
Log ( 1 + x ) = 
Log (1 - x) = 
- …
Log ( 1 – x2) = -2 [
.] ------(1)
Now ,
Log ( 
) = 2 [
.]
=2 x[ 
.] ----(2)
Replacing eq1 and eq2 in S, here x = ½
S = -1/2 log ( 1 – ¼ ) + 1/( 2 x ½) log ( 1 + ½ / 1 – ½ )
S = -½ log ( ¾ ) + log ( 3 )
S = -½ log ( 3 ) + ½ log ( 4) + log ( 3 )
S = ½ log ( 3 ) + ½ log ( 4)
S = ½ log ( 12 )
S = log √12
Therefore, the correct answer is log log√12
In this question, we have to find the sum of the series. Separate the series in even and odd series, and replace with Log ( 1 – x2) and Log ( 1 + x / 1-x ) .
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