a, 2S=2+\(2^2\)+\(2^3+...+2^{201}\)

2S-S=S=\(2^{201}-1\)

câu b thì nhân 3 rồi làm tương tự nha. tiickk mik vs

a, S = 1 + 2 + 2² + 2³ + ... + 2²⁰¹⁷

Ta có : 2S = 2 + 2² + 2³ +.... + 2²⁰¹⁸

Lấy 2S - S ta được : S = 2²⁰¹⁸ - 1

b, Đặt S = 3 + 3² + 3³ + ... + 3²⁰¹⁷

Ta có : 3S = 3² + 3³ + ... + 3²⁰¹⁸

Lấy 3S - S ta được 2S = 3²⁰¹⁸ -3 

=> \(S=\frac{3^{2018}-3}{2}\)

c, Đặt S = 4 + 4² + 4³ + ... + 4²⁰¹⁷ 

Ta có : 4S = 4² + 4³ + ... + 4²⁰¹⁸

Lấy 4S - S ta được 3S = 4²⁰¹⁸ - 4 

=> \(S=\frac{4^{2018}-4}{3}\)

a, S = 1 + 2 + 22 + 23 + ... + 22017

Ta có : 2S = 2 + 22 + 23 +.... + 22018

Lấy 2S - S ta được : S = 22018 - 1

b, Đặt S = 3 + 32 + 33 + ... + 32017

Ta có : 3S = 32 + 33 + ... + 32018

Lấy 3S - S ta được 2S = 32018 -3 

=> �=32018−32S=232018−3​

c, Đặt S = 4 + 42 + 43 + ... + 42017 

Ta có : 4S = 42 + 43 + ... + 42018

Lấy 4S - S ta được 3S = 42018 - 4 

=> �=42018−43S=342018−4​
 

\(a)\) \(S=1+2+2^2+2^3+...+2^{2017}\)

\(2S=2+2^2+2^3+2^4+...+2^{2018}\)

\(2S-S=\left(2+2^2+2^3+2^4+...+2^{2018}\right)-\left(1+2+2^2+2^3+...+2^{2017}\right)\)

\(S=2^{2018}-1\)

\(b)\) \(S=3+3^2+3^3+...+3^{2017}\)

\(3S=3^2+3^3+3^4+...+3^{2018}\)

\(3S-S=\left(3^2+3^3+3^4+...+3^{2018}\right)-\left(3+3^2+3^3+...+3^{2017}\right)\)

\(2S=3^{2018}-3\)

\(S=\frac{3^{2018}-3}{2}\)

\(c)\) \(S=4+4^2+4^3+...+4^{2017}\)

\(4S=4^2+4^3+4^4+...+4^{2018}\)

\(4S-S=\left(4^2+4^3+4^4+...+4^{2018}\right)-\left(4+4^2+4^3+...+4^{2017}\right)\)

\(3S=4^{2018}-4\)

\(S=\frac{4^{2018}-4}{3}\)

\(d)\) \(S=5+5^2+5^3+...+5^{2017}\)

\(5S=5^2+5^3+5^4+...+5^{2018}\)

\(5S-S=\left(5^2+5^3+5^4+...+5^{2018}\right)-\left(5+5^2+5^3+...+5^{2017}\right)\)

\(4S=5^{2018}-5\)

\(S=\frac{5^{2018}-5}{2}\)

Chúc em học tốt ~ 

Tks anh ạ 

Trả lời

a)

\(S=1+2+2^2+2^3+...+2^{2017}\)

\(\Rightarrow2S=2\left(1+2+2^2+2^3+...+2^{2017}\right)\)

\(\Rightarrow2S=2+2^2+2^3+2^4+...+2^{2018}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+2^4+...+2^{2018}\right)-\left(1+2+2^2+2^3+...+2^{2017}\right)\)

\(\Rightarrow S=2^{2018}-1\)

b)

\(S=3+3^2+3^3+...+3^{2017}\)

\(3S=3^2+3^3+3^4+...+3^{2018}\)

\(3S-S=\left(3^2+3^3+3^4+...+3^{2018}\right)-\left(3+3^2+3^3+...+3^{2017}\right)\)

\(2S=3^{2018}-3\)

\(S=\frac{3^{2018}-3}{2}\)

c)

\(S=4+4^2+4^3+...+4^{2017}\)

\(4S=4^2+4^3+4^4+...+4^{2018}\)

\(4S-S=\left(4^2+4^3+4^4+...+4^{2018}\right)-\left(4+4^2+4^3+...+4^{2017}\right)\)

\(3S=4^{2018}-4\)

\(S=\frac{4^{2018}-4}{3}\)

d)

\(S=5+5^2+5^3+...+5^{2017}\)

\(5S=5^2+5^3+5^4+...+5^{2018}\)

\(5S-S=\left(5^2+5^3+5^4+...+5^{2018}\right)-\left(5+5^2+5^3+...+5^{2017}\right)\)

\(4S=5^{2018}-5\)

\(S=\frac{5^{2018}-5}{4}\)

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

=> 5S=5^2+5^3+5^4+...5^100

=> 5S-S=4S=(5^2+5^3+5^4+...5^100)-(5+5^2+5^3+5^4+...5^99)

=> 4S = 5¹⁰⁰-5

=> S=(5¹⁰⁰-5)/4

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

=> S=5^1+2+3+...+99

=> S=5^{((99+1).99):2}

=> S=5⁴⁹⁵⁰

(3x-2)+16=125+12

(3x-2)+16=137

3x-2=121

3x=123

x=41

5s=5^2+5^3+5^4+5^5+......+5^100

5s-s=5^100-5

4s=5^100-5

s=(5^100-5):4

kick nhé

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

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

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

`S=4+3^{2} +3^{3}+...+3^{223}`

`=>3S=12+3^{3}+3^{4}+....+3^{224}`

Có: \(3S-S=12+3^{3}+3^{4}+....+3^{224}-4-3^{2}-3^{3}-...-3^{233}\)

 `=>2S=12+3^{224}-4-3^2`

\(=>S=4+\dfrac{3^{224}-3^{2}}{2}\)