Interesting Summation

Algebra Level 5

When MM is a digit, M+MM+MMM++MMMMn M’s=Ma[10n+1109n].M + \overline{MM} + \overline{MMM} + \cdots + \underbrace{\overline{MMM\cdots M}}_{n \ M\text{'s}} = \frac{M}{a}\left [ 10^{n+1}-10-9n \right ]. Find the value of a.a.

Note that MM\overline{MM} represents a two-digit number with both digits being M.M.

×

Problem Loading...

Note Loading...

Set Loading...