The sum to infinity of the series 1+(4/5)+(7/52)+(10/53)+ ldots is

Question

The sum to infinity of the series 1+(4/5)+(7/52)+(10/53)+ ldots is (A) (16/25) (B) (11/5) (C) (35/16) (D) (8/11)

Tardigrade Admin · Accepted Answer

S=1+(4/5)+(7/52)+(10/53)+ ldots +∞ ... (1) (S/5)=0+(1/5)+(4/52)+(7/53)+ ldots +∞ ... (2) On subtracting both the eq (1) and (2), we get, (4/5)S=1+(3/5)+(3/52)+ ldots +∞ S=(35/16)

Q. The sum to infinity of the series $1 + \frac{4}{5} + \frac{7}{5 ^{2}} + \frac{10}{5 ^{3}} + \dots$ is

$\frac{16}{25}$

$\frac{11}{5}$

$\frac{35}{16}$

$\frac{8}{11}$

Q. The sum to infinity of the series 1+54​+527​+5310​+… is

2516​

511​

1635​

118​

S=1+54​+527​+5310​+…+∞ ... (1) 5S​=0+51​+524​+537​+…+∞ ... (2) On subtracting both the eq (1) and (2), we get, 54​S=1+53​+523​+…+∞ S=1635​

Q. The sum to infinity of the series $1 + \frac{4}{5} + \frac{7}{5 ^{2}} + \frac{10}{5 ^{3}} + \dots$ is

$\frac{16}{25}$

$\frac{11}{5}$

$\frac{35}{16}$

$\frac{8}{11}$