Home -> Solved problems -> Why 9.9999999…=10
Why 9.9999999...=10
Solution
Solution by Leonhard Euler:
\[9,999 \ldots = 9+\frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+\cdots\]
\[=9\left(1+\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\cdots\right)\]
\[=9 \frac{1}{1-\frac{1}{10}}\]
\[=9 \frac{10}{9}\]
\[=10\]
Home -> Solved problems -> Why 9.9999999…=10
Every problem you tackle makes you smarter.
↓ Scroll down for more maths problems↓
Find the equation of the curve formed by a cable suspended between two points at the same height
Prove that the function \(f(x)=\frac{x^{3}+2 x^{2}+3 x+4}{x}
\) has a curvilinear asymptote \(y=x^{2}+2 x+3\)
Why does the number \(98\) disappear when writing the decimal expansion of \(\frac{1}{9801}\) ?
if we draw an infinite number of circles packed in a square using the method shown below, will the sum of circles areas approach the square's area?
Is it possible to solve for \(x\) so that \(ln(x)\), \(ln(2x)\), and \(ln(3x)\) form a right triangle?