Question

The value of $\frac{1}{0.8} + \frac{1}{0.08} + \frac{1}{0.008} + \dots\dots$ up to the seventh term is ______.

• A. 138888.25
• B. 138888.75
• C. 1388888.75
• D. 13888888.75

Answer 1

Answer:

C. 1388888.75

The value of the expression up to the seventh term is 1,388,888.75.

Step 1: Simplify each term
Convert each decimal in the denominator into a standard number:

• 1st term: $\frac{1}{0.8} = \frac{10}{8} = 1.25$

• 2nd term: $\frac{1}{0.08} = \frac{100}{8} = 12.5$

• 3rd term: $\frac{1}{0.008} = \frac{1000}{8} = 125$

Following this geometric pattern, the remaining terms are:

• 4th term: $1,250$

• 5th term: $12,500$

• 6th term: $125,000$

• 7th term: $1,250,000$

---

Step 2: Add all seven terms together
$1.25 + 12.5 + 125 + 1,250 + 12,500 + 125,000 + 1,250,000$

You can easily calculate this by factoring out $1.25$:
$= 1.25 \times (1 + 10 + 100 + 1,000 + 10,000 + 100,000 + 1,000,000)$
$= 1.25 \times 1,111,111$
$= \mathbf{1,388,888.75}$