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 – x^{2}) = -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 – x^{2}) and Log ( 1 + x / 1-x ) .

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