\(A=5+5^2+....+5^{101}\)
\(\Rightarrow5A=5^2+5^3+....+5^{102}\)
\(\Rightarrow5A-A=4A=\left(5^2+5^3+....+5^{102}\right)-\left(5+5^2+....+5^{101}\right)\)
\(\Rightarrow4A=5^{102}-5\)
\(\Rightarrow A=\frac{5^{102}-5}{4}\)
Rút gọn.
\(A=5+5^2+5^3+...+5^{101}\)
Rút gọn lũy thừa:
A = \(\frac{8^5\cdot\left(-5\right)^8+2^5\cdot10}{2^{16}\cdot5^7+20^8}^9\)
Rút gọn :
\(\left|x-3\right|+\left|4+x\right|+x-5=Q\)
Rút gọn phân số
a) \(\dfrac{-1997.1996+1}{\left(-1995\right).\left(-1997\right)+1996}\)
b)\(\dfrac{\left(-5\right)^{3^{ }}.40.4^3}{135.\left(-2\right)^{14}.\left(-100\right)^0}^{ }\)
a) Rút gọn : \(M=5+5^2+5^3+...+5^{100}\)
b) Chứng tỏ : \(N=5^1+5^2+5^3+5^4+...+5^{2010}⋮6\) và \(31\)
a) Rút gọn : \(M=5+5^2+5^3+...+5^{100}\)
b) Chúng tỏ : \(N=5^1+5^2+5^3+5^4+...+5^{2010}⋮6\)và \(31\)
Rút gọn:
a) 2^12.3^5-4^6.3^6/2^12+9^3+8^4.3^5
B) 49^6.5-7^11/(-7)^10.5-2.49^5
Tính :
\(\left(\frac{3}{5}-\frac{1}{2}+\frac{7}{3}\right)-\left(\frac{1}{3}-\frac{5}{2}+\frac{1}{5}\right)-\left(-\frac{3}{5}+3-\frac{5}{3}\right)\)