Question

cho S = 3^2 + 3^4 +...+ 3^998 + 3^1000

a) tính S

b) CMR S chia 7 dư 6

giúp mik trình bày phần a nhé!

 

Answer 1

a) 9.S = 3⁴+ 3⁶+.....+ 3¹⁰⁰⁰+ 3¹⁰⁰²

9.S - S = (3⁴+ 3⁶+.....+ 3¹⁰⁰⁰+ 3¹⁰⁰²) - ( 3²+ 3⁴+.....+ 3⁹⁹⁸+ 3¹⁰⁰⁰)

8.S = 3¹⁰⁰² - 3²

 S =3¹⁰⁰² - 3² / 8

Answer 2

a) \(S=3^2+3^4+...+3^{998}+3^{1000}\)

\(\Rightarrow3^2.S=3^2.3^2+3^2.3^4+...+3^2.3^{998}+3^2.3^{1000}\)

\(9S=3^4+3^6+...+3^{1000}+3^{1002}\)

\(\Rightarrow8S=9S-S=\left(3^4+3^6+...+3^{1000}+3^{1002}\right)-\left(3^2+3^4+...+3^{998}+3^{1000}\right)\)

\(=3^{1002}-3^2\)

\(=3^{1002}-9\)

\(\Rightarrow S=\dfrac{3^{1002}-9}{8}\)