Question

find ln [ 1 +1/2+1/4+1/8+.........]
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Answer 1

GIVEN :–

A series ➪ [ 1 + ½ + ¼ + ⅛ + ........ ]

TO FIND :–

Value of given series.

SOLUTION :–

• Let's assume that given series have n terms .

⮕ Given series maintain a Geometrical progression.

➨ First term of G.P. (a) = 1

Common ratio (r) = ½

${ \bold{ \implies{sum \: \: of \: \:G.P. \: = \frac{a( {r}^{n} - 1)}{(r - 1)} }}}$

➨ Sum of G.P. = [{1(½)ⁿ - 1}/{½ - 1}]

Sum of G.P. = (-2) [ (½)ⁿ - 1 ]

• If n –> ∞ , then –

➨ Sum = a /(1 - r)

Sum = (1)/(1 - ½)

Sum = 2

Answer 2

Step-by-step explanation:

answer is ln2. good question. and good use of sequence and series