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The simplification of $$\frac{1}{8} + $$ $$\frac{1}{{{8^2}}} + $$ $$\frac{1}{{{8^3}}} + $$ $$\frac{1}{{{8^4}}} + $$ $$\frac{1}{{{8^5}}}$$ upto three place of decimals yields = ?
Answer & Solution
Correct Answer:
Option
A
$$\eqalign{
& {\text{According to question,}} \cr
& \frac{1}{8} + \frac{1}{{{8^2}}} + \frac{1}{{{8^3}}} + \frac{1}{{{8^4}}} + \frac{1}{{{8^5}}} \cr
& \Rightarrow \frac{1}{8} + \frac{1}{{64}} + \frac{1}{{512}} + \frac{1}{{4096}} + \frac{1}{{32768}} \cr} $$
⇒ 0.125 + 0.015625 + 0.00195313 + 0.00024414 + 0.0000305175
⇒ 0.143
⇒ 0.125 + 0.015625 + 0.00195313 + 0.00024414 + 0.0000305175
⇒ 0.143
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