Câu hỏi của Chí Tiến

Question

Rút gọn: A = 1 + 5 + 52 + 53 + ...... + 549 + 550

Trần Hương Thoan · Accepted Answer

$A=1+5+5^2+5^3+....+5^{49}+5^{50}$

$5A=5+5^2+5^3+5^4+.....+5^{50}+5^{51}$

$5A-A=5+5^2+5^3+5^4+......+5^{50}+5^{51}-\left(1+5+5^2+5^3+......+5^{49}+5^{50}\right)$

$4A=5+5^2+5^3+5^4+......+5^{50}+5^{51}-1-5-5^2-5^3-5^4-.....-5^{49}-5^{50}$

$4A=5^{51}-1$

$A=\frac{5^{51}-1}{4}$Câu trả lời: $A=1+5+5^2+5^3+....+5^{49}+5^{50}$

$5A=5+5^2+5^3+5^4+.....+5^{50}+5^{51}$

$5A-A=5+5^2+5^3+5^4+......+5^{50}+5^{51}-\left(1+5+5^2+5^3+......+5^{49}+5^{50}\right)$

$4A=5+5^2+5^3+5^4+......+5^{50}+5^{51}-1-5-5^2-5^3-5^4-.....-5^{49}-5^{50}$

$4A=5^{51}-1$

$A=\frac{5^{51}-1}{4}$