Đáp án:
Giải thích các bước giải:
B = 5 + $5^{2}$ + $5^{3}$ + $5^{4}$ + $5^{5}$ + $5^{6}$ + ..... + $5^{2011}$ + $5^{2012}$ + $5^{2013}$
B = ( 5 + $5^{2}$ + $5^{3}$ ) + ( $5^{4}$ + $5^{5}$ + $5^{6}$ ) + ..... + ( $5^{2011}$ + $5^{2012}$ + $5^{2013}$ )
B = 5 . ( 1 + 5 + $5^{2}$ ) + $5^{4}$ . ( 1 + 5 + $5^{2}$ ) + ..... + $5^{2011}$ . ( 1 + 5 + $5^{2}$ )
B = 5 . 31 + $5^{4}$ . 31 + ..... + $5^{2011}$ . 31
B = 31 . ( 5 + $5^{4}$ + ..... + $5^{2011}$ )
Vì 31 . ( 5 + $5^{4}$ + ..... + $5^{2011}$ ) chia hết cho 31
→ B chia hết cho 31