Question

(3.x-2)^2+4^2=5^3+3.2^2

tính giá trị biểu thức:

S=5+5^2+5^3+5^4+...5^99

S=5*5^2*5^3*5^4*...5^99

mik học íu mog các bn giúp mik vs

Answer 1

\(\left(3x-2\right)^2+4^2=5^3+3.2^2\\ \Rightarrow\left(3x-2\right)^2+16=125+12\\ \Rightarrow\left(3x-2\right)^2=121\\ \Rightarrow3x-2=11\\ \Rightarrow x=\frac{13}{3}\)

S= \(5+5^2+5^3+.....+5^{99}\\ \Rightarrow5S=5^2+5^3+5^4+.....+5^{100}\\ \Rightarrow4S=5^{100}-5\\ \Rightarrow\frac{5^{100}-5}{4}\)

S=\(5.5^2.5^3.5^4.........5^{99}=5^{1+2+3+4+....+99}=5^{4950}\)

 

Answer 2

S=5+5²+5³+5⁴+...+5⁹⁹

5S=5²+5³+5⁴+...+5⁹⁹

5S-S=(5²-5²)+(5³-5³)+...+(5⁹⁹-5⁹⁹⁾+5¹⁰⁰+5

S=(5¹⁰⁰+5⁾:4