Sequence

Algebra Level 1

0.45 + 0.0045 + 0.000045 + ⋯ = ? 0.45+0.0045+0.000045+ \cdots = \ ?


The answer is 0.45454545.

Akwesi Barnes by akwesi barnes , 22, Ghana

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2 solutions

The sequence can be added like this,

0.45 + 0.0045 + 0.000045 + 0.00000045 + 0.0000000045 \quad 0.45\\ +0.0045\\ +0.000045\\ +0.00000045\\ +0.0000000045

This will invariably result in a sum equal to 0.454545454545454545.... 0.454545454545454545....

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Sum of geometric progression with infinitely many terms.

a = 0.45 , r = 0.0045 0.45 = 0.000045 0.0045 = 0.01 a=0.45,r=\dfrac{0.0045}{0.45}=\dfrac{0.000045}{0.0045}=0.01

S = a 1 − r = 0.45 1 − 0.01 = 0.45454545 S=\dfrac{a}{1-r}=\dfrac{0.45}{1-0.01=0.45454545}

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