Question

1+(0.4)+(0.04)*+............=. a)24÷25. b)25÷24. c)4÷25. d)25÷4

Answer 1

1 + (0.4) + (0.04) + (0.004) +.......

=1 + 4{ 1/10 + 1/10² + 1/10³ + 1/10⁴ +....}

here ,

1/10 + 1/10² + 1/10³ + 1/10⁴ +.....

this is in geometric form so,
for sum of infinte number in geometric
= a/(1 - r)

where a = first term in GP
r = geometric ratio or common ratio

now ,
a = 1/10 and r = 1/10
then,
S = 1/10/( 1-1/10) = 1/9

so, sum = 1 + 4S = 1 + 4× 1/9 = 13/9

I think option may be incorrect ,
because answer is 13/9