Frightening Fractions For Fun

Algebra Level pending

We have a sequence: x 10 + x 1 0 2 + x 1 0 3 + . . . . \frac{x}{10} + \frac{x}{10^2} + \frac{x}{10^3} + .... What does this sequence add up to?

10 x/9 Not able to solve with the given information x.x \sqrt{x}

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2 solutions

Vyom Jain
Apr 16, 2015

can be done with the help of infinite summation of a decreasing GP

this gives x[(1/10)/{1-(1/10)}]

= x/9

Lets start simple. x/(10) + x/(10^2) = (10x+x)÷100=11x/100. 11x/100 + x/1000 =(110x+x) ÷ 1000 = 111x/1000. 111x/1000 --> 1111x/10,000… 1/9. Just find common denominator.

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