Question

Tinh:a)N=1+3^2+...+3^100;b)P=1+5^3+5^6+5^9+...+5^99

Answer 1

a)(nhân N vs 3^2 rồi trừ đi N) chia cho 3^2-1

b)(nhân P vs 5^3 rồi trừ đi P) chia cho 5^3-1

Answer 2

a, \(N=1+3^2+...+3^{100}\)

\(\Rightarrow3^2N=3^2+3^4+...+3^{102}\)

\(\Rightarrow3^2N-N=\left(3^2+3^4+...+3^{102}\right)-\left(1+3^2+...+3^{100}\right)\)

\(\Rightarrow8N=3^{102}-1\)

\(\Rightarrow N=\frac{3^{102}-1}{8}\)

Answer 3

\(P=1+5^3+5^6+...+5^{99}\)

\(5^3P=5^3+5^6+5^9+...+5^{102}\)

\(5^3P-P=\left(5^3+5^6+5^9+...+5^{102}\right)-\left(1+5^3+5^6+...+5^{99}\right)\)

\(124P=5^{102}-1\)

\(P=\frac{5^{102}-1}{124}\)