S = 3⁰ + 3¹ + 3² + ... + 3²⁰¹⁶
3S = 3¹ + 3² + 3³ + ... + 3²⁰¹⁶ + 3²⁰¹⁷
3S - S = ( 3¹ + 3² + 3³ + ... + 3²⁰¹⁶ + 3²⁰¹⁷ ) - ( 3⁰ + 3¹ + 3² + ... + 3²⁰¹⁶ )
2S = 3²⁰¹⁷ - 3⁰
2S = 3²⁰¹⁷ - 1
S = \(\dfrac{3^{2017}-1}{2}\)

N = \(\dfrac{3}{5.7}+\dfrac{3}{7.9}+\dfrac{3}{9.11}+...+\dfrac{3}{197.199}\)
N = \(\dfrac{3}{2}.\left(\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+...+\dfrac{2}{197.199}\right)\)
N = \(\dfrac{3}{2}.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{197}-\dfrac{1}{199}\right)\)
N = \(\dfrac{3}{2}.\left(\dfrac{1}{5}-\dfrac{1}{199}\right)\)
N = \(\dfrac{3}{2}.\dfrac{194}{995}\)
N = \(\dfrac{291}{995}\)

a) \(2^{4x}-3^{2x}=144-164:41\)

\(\Leftrightarrow16^x-9^x=144-4\)

\(\Leftrightarrow\) ......

bjan tự tính tiếp đc òi                 

1) Quãng đường AB là :
\(36\dfrac{1}{4}\)km/h . 3.2h = 116 ( km )
Thời gian người ấy đi từ A đến B lúc về là :
116 : 40 = 2.9 ( giờ )
Đ/S : 2.9 giờ

Đề sai. câu đầu phải là \(\dfrac{1}{18.21}\) mới đúng.
Nếu câu đầu là \(\dfrac{1}{18.21}\) thì mik có cách làm sau :
\(\dfrac{1}{18.21}+\dfrac{1}{21.24}+\dfrac{1}{24.27}+...+\dfrac{1}{123.126}\)

= \(\dfrac{1}{3}.\left(\dfrac{3}{18.21}+\dfrac{3}{21.24}+\dfrac{3}{24.27}+...+\dfrac{3}{123.126}\right)\)

= \(\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{27}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)

= \(\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{126}\right)\)

= \(\dfrac{1}{3}.\dfrac{1}{21}\)

= \(\dfrac{1}{63}\)

10235

tick nha Lucy Mk K Cs P

Ta có :
\(B=\dfrac{10^{2008}+1}{10^{2009}+1}< \dfrac{10^{2008}+1+9}{10^{2009}+1+9}\)
Biến đổi vế trái:
\(\dfrac{10^{2008}+10}{10^{2009}+10}\)= \(\dfrac{10.\left(10^{2007}+1\right)}{10.\left(10^{2008}+1\right)}\)= \(\dfrac{10^{2007}+1}{10^{2008}+1}\)= A
Suy ra:
A > B.

A > B

\(B=\dfrac{2017^{18}+1}{2017^{17}+1}< \dfrac{2017^{18}+1+2016}{2017^{17}+1+2016}\)
Mà \(\dfrac{2017^{18}+1+2016}{2017^{17}+1+2016}=\dfrac{2017^{18}+2017}{2017^{17}+2017}=\dfrac{2017.\left(2017^{17}+1\right)}{2017.\left(2017^{16}+1\right)}=\dfrac{2017^{17}+1}{2017^{16}+1}=A\)
=> B < A hay :
A < B