Question

tính : A=5 +5 mũ3+5mũ 5+5 mũ7+.......+ 5 mũ 49+5 mũ 51

Answer 1

\(A=5+5^3+5^5+5^7+...+5^{49}+5^{51}\\ =>5^2.A=5^3+5^5+5^7+5^9+...+5^{51}+5^{53}\\ =>25A-A=\left(5^3+5^5+5^7+5^9+...+5^{51}+5^{53}\right)-\left(5+5^3+5^5+5^7+...+5^{49}+5^{51}\right)\\ =>24A=5^{53}-5\\ =>A=\dfrac{5^{53}-5}{24}\)

Answer 2

\(A=5+5^3+5^5+...+5^{49}+5^{51}\)

\(25A=5^3+5^5+5^7+...+5^{51}+5^{53}\)

\(25A-A=5^3+5^5+5^7+...+5^{51}+5^{53}-\left(5+5^3+5^5+...+5^{49}+5^{51}\right)\)

\(24A=5^{53}-5\)

\(A=\dfrac{5^{53}-5}{24}\)

Answer 3

A=5+53+55+57+...+549+551=>52.A=53+55+57+59+...+551+553=>25A−A=(53+55+57+59+...+551+553)−(5+53+55+57+...+549+551)=>