\(S=\dfrac{2^2}{1.2}+\dfrac{2^2}{2.3}+\dfrac{2^2}{3.4}+...+\dfrac{2^2}{2022.2023}\)

\(S=2^2.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2022.2023}\right)\)

\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\right)\)

\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2023}\right)\)

\(S=2^2.\dfrac{2022}{2023}\)

\(S=\dfrac{2^2.2022}{2023}=\dfrac{8088}{2023}\)

\(B=1+2+2^2+...+2^6.\)

\(=>4B=2^2+2^3+...+2^8\)\(\left(1\right)\)

\(A=2^2+2^3+...+2^8\)\(\left(2\right)\)

Từ (1) và (2) 

=> A = 4B

\(A=2^{100}-2^{99}-...-2^2-2\)

\(2A=2^{101}-2^{100}-...-2^3-2^2\)

\(2A-A=2^{101}-2^{100}-...-2^3-2^2-2^{100}+2^{99}+...2^2+2\)

\(A=2^{101}-\left(2^{100}-2^{100}+2^{99}-2^{99}+...+2^2-2^2+-2\right)\)

\(A=2^{101}+2\)

2²s=2+2²+...+2²⁰²⁰

4S-S=(2+2²+...+2²⁰²⁰⁾-(1+2+2²+....+2²⁰¹⁸)

3S=2²⁰²⁰-1

S=(2²⁰²⁰-1):3

cảm ơn cậu 

\(S=1+2+2^2+...+2^{2018}\)

\(\Rightarrow2S=2+2^2+2^3+...+2^{2019}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+...+2^{2019}\right)-\left(1+2+2^2+...+2^{2018}\right)\)

\(\Rightarrow S=2^{2019}-1\)

Vậy...(tự kết luận)

:)))

đáp số 3/5 đó bạn

3 phan 5

S = 22 + 42 + 62 + ... + 202

   = (2.1)2 + (2.2)2 + (2.3)2 ... (2.10)2

   = 22.12 + 22.22 + 22.32 + ... + 22.102

   = 22 (12 + 22 + ... + 102 )

   = 4 . 385

   = 1540

3/5 tick di anh dai gia

3/5chac chan cho minh di