The sum of the first 20 terms of the series 1 + (3/2) + (7/4)+ (15/8)+(31/16)+ dots , is :

Question

The sum of the first 20 terms of the series 1 + (3/2) + (7/4)+ (15/8)+(31/16)+ dots , is : (A) 38+(1/219) (B) 38+(1/220) (C) 39+(1/220) (D) 39+(1/219)

Tardigrade Admin · Accepted Answer

Given: 1+(3/2)+(7/4)+ (15/8)+(31/6)+⋅s =(2-1)+(2-(1/2))+(2-(1/4))+(2-(1/8))+(2-(1/16))+ dots up to 20 terms =40-(1+(1/2)+(1/4)+(1/8)+ dots up to 20 terms ) =40-((1-((1/2))20/1-(1)2)) =40-2+(1/219)=38+(1/219)

Q. The sum of the first 20 terms of the series $1 + \frac{3}{2} + \frac{7}{4} + \frac{15}{8} + \frac{31}{16} + \dots$ , is :

$38 + \frac{1}{2 ^{19}}$

$38 + \frac{1}{2 ^{20}}$

$39 + \frac{1}{2 ^{20}}$

$39 + \frac{1}{2 ^{19}}$

Q. The sum of the first 20 terms of the series 1+23​+47​+815​+1631​+… , is :

38+2191​

38+2201​

39+2201​

39+2191​

Given: 1+23​+47​+815​+631​+⋯ =(2−1)+(2−21​)+(2−41​)+(2−81​)+(2−161​)+… up to 20 terms =40−(1+21​+41​+81​+… up to 20 terms ) =40−(1−21​1−(21​)20​) =40−2+2191​=38+2191​

Q. The sum of the first 20 terms of the series $1 + \frac{3}{2} + \frac{7}{4} + \frac{15}{8} + \frac{31}{16} + \dots$ , is :

$38 + \frac{1}{2 ^{19}}$

$38 + \frac{1}{2 ^{20}}$

$39 + \frac{1}{2 ^{20}}$

$39 + \frac{1}{2 ^{19}}$