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Efectuați:10 +100 +1000 +10000 +...... +1000000000

Răspuns :

S=10 +100 +1000 +10000 +...... +1000000000
S=10¹ +10² +10³ +10⁴ +...... +10⁹    *10
10S=10² +10³ +10⁴ +...... +10⁹+10¹⁰  +10 - 10
10S=10+10² +10³ +10⁴ +...... +10⁹+10¹⁰   - 10
10S=S+10¹⁰  - 10
10S-S=10¹⁰  - 10
9S=10¹⁰  - 10
S=
(10¹⁰  - 10)/9