The 9's sum

Algebra Level pending

What is the value of the following sum?

9 + 99 + 999 + 9999 + . . . + 999999999 9+99+999+9999+...+999999999

1111111011 1111111101 1111110111 1111101111

Daniel Nguyễn by Daniel Nguyễn , 22, Vietnam

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1 solution

Vishal S
Jan 6, 2015

9+99+999+9999+99999+......999999999 = 9(1+11+111+1111+....111111111)

⇒ \Rightarrow 9(123456789)

⇒ \Rightarrow 1111111101

Therefore 9+99+999+9999+.....+999999999= 1111111101 \boxed{1111111101}

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