\(A=5+5^2+...+5^{30}\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right)\)
\(A=\left(5+25\right)+5\cdot\left(5+25\right)+...+5^{28}\cdot\left(5+25\right)\)
\(A=30+5\cdot30+...+5^{28}\cdot30\)
\(A=30\cdot\left(1+5+...+5^{28}\right)\)
Vậy A chia hết cho 30
\(A=5+5^2+....+5^{30}\)
\(A=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+...+\left(5^{28}+5^{29}+5^{30}\right)\)
\(A=5\cdot\left(1+5+25\right)+5^4\cdot\left(1+5+25\right)+...+5^{28}\cdot\left(1+5+25\right)\)
\(A=5\cdot31+5^4\cdot31+...+5^{28}\cdot31\)
\(A=31\cdot\left(5+5^4+...+5^{28}\right)\)
Vậy A chia hết cho 31
\(A=5+5^2+...+5^{30}\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right)\)
\(A=5\cdot\left(1+5\right)+5^3\cdot\left(1+5\right)+...+5^{29}\cdot\left(1+5\right)\)
\(A=5\cdot6+5^3\cdot6+...+5^{29}\cdot6\)
\(A=6\cdot\left(5+5^3+...+5^{29}\right)\)
Vậy A chia hết cho 6
Đặt \(A=5\text{+}5^2\text{+}5^3\text{+}....\text{+}5^{30}\)
\(\left(5\text{+}5^2\right)\text{+}\left(5^3\text{+}5^4\right)\text{+}....\left(5^{29}\text{+}5^{30}\right)\)
\(5.\left(1+5\right)\text{+}5^3\left(1+5\right)\text{+}....5^{29}.\left(1\text{+}5\right)\)
\(\left(1+5\right)\left(5\text{+}5^3\text{+}....\text{+}5^{29}\right)\)
\(6.\left(5\text{+}5^3\text{+}....5^{29}\right)⋮6\left(dpcm\right)\)
Phong chỉ cần chia hết cho 30 là đã chia hết cho 6 rồi bạn
....................... = A = 6(5 + 53 +...+ 529) ⋮ 6
....................... = A = 30(1 + 5 +...+ 528) ⋮ 30
....................... = A = 31( 5 + 54 +...+ 528) ⋮ 31
Chúc bạn học tốt!
Mình ko có thời gian ghi hết nên bạn có thể tham khảo phong nhá!
