Question : If $A =(\frac{1}{0.4})+(\frac{1}{0.04})+(\frac{1}{0.004})+....$ upto 8 terms, then what is the value of $A$?
Option 1: 27272727.5
Option 2: 25252525.5
Option 3: 27777777.5
Option 4: 25555555.5
Correct Answer: 27777777.5
Solution :
Given: $ A =(\frac{1}{0.4})+(\frac{1}{0.04})+(\frac{1}{0.004})+....$ upto 8 terms.
This expression can be written as:
$⇒ A =(\frac{10}{4})+(\frac{100}{4})+(\frac{1000}{4})+(\frac{10000}{4})+(\frac{100000}{4})+(\frac{1000000}{4})(\frac{10000000}{4})+(\frac{100000000}{4})$
Using the formula, $S_n = \frac{a(r^n-1)}{r-1}$, where $a$ = first term, $r$ = common ratio, $n$ = number of terms
$10 + 100 + 1000+ .............+ 100000000 = \frac{10(10^8-1)}{10-1}=111111110$
$⇒ A=(\frac{111111110}{4})$
$\therefore A = 27777777.5$
Hence, the correct answer is 27777777.5.
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