Vrijeme: 23:16

Nepotrebno bezobrazni | Unnecessarily rude #1

Svaki zadatak ovog lanca će izgledati ovako:

Odredi A \pmod{B} gdje će A i B biti prirodni.

Tako ćemo označavati ostatak pri dijeljenju broja A s brojem B. Na primjer, 5 \pmod{2} = 1 i 73 \pmod{10} = 3.
Odredi:

1 + 11 + 111 + 1111 +  \dots + \underbrace{111\dots111}_{ \underbrace{11\dots11}_{111 \;\text{jedinica}} \;\text{jedinica} } \pmod{10^9}

Every task within this chain will look like this:

Determine A \pmod{B} where A and B are positive integers.

This is how we will denote the remainder when A is divided by B. For example, 5 \pmod{2} = 1 i 73 \pmod{10} = 3.
Determine:

1 + 11 + 111 + 1111 +  \dots + \underbrace{111\dots111}_{ \underbrace{11\dots11}_{111 \;\text{ones}} \;\text{ones} } \pmod{10^9}