The sum value of the infinite series 1+(1/5)+(1/25)+(1/125)+(1/625)+....∞ is

Question

The sum value of the infinite series 1+(1/5)+(1/25)+(1/125)+(1/625)+....∞ is (A)  (4/5)  (B)  (5/4)  (C)  (3/2)  (D) indefinite

Tardigrade Admin · Accepted Answer

The given series is, 1 +(1/5) + (1/52) + (1/53) + .....∞ which is a G.P. with first term (a) = 1 and common ratio (r) = (1/5) ∴ Sum of infinite terms = (1/1- (1)5) = (5/4)

Q. The sum value of the infinite series $1 + \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + ....\infty$ is

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{3}{2}$

indefinite

The given series is,
$1 + \frac{1}{5} + \frac{1}{5 ^{2}} + \frac{1}{5 ^{3}} + .....\infty$
which is a $G . P .$ with first term $(a) = 1$
and common ratio $(r) = \frac{1}{5}$
$∴$ Sum of infinite terms $= \frac{1}{1 - \frac{1}{5}} = \frac{5}{4}$

Q. The sum value of the infinite series 1+51​+251​+1251​+6251​+....∞ is

54​

45​

23​