Đặt \(A=\)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)

\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\)

\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)

\(2A=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)

\(A=\frac{5}{39}\)

Câu còn lại cx dựa như vậy nhé bn ! 

Chúc bn hc tốt <3

câu c hình như sai đề hả bn

2/15+2/35+2/63+.....+2/9603=2/3.5+2/5.7+2/7.9+...2/97.99

=1/3-1/5+1/5-1/7+...+1/97-1/99

=1/3-1/99

=33/99-1/99

=32/99

\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{9603}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)

S>5 . 2⁹⁸

A = 1 + 2 + 2² + 2³ + .... +2⁹⁸

2A = 2(1 + 2 + 2² + 2³ +....+2⁹⁸)

2A = 2 + 2² + 2³ + 2⁴ +....+2⁹⁹

2A - A = (2 + 2² + 2³ + 2⁴ +.....+ 2⁹⁹) - (1 + 2 + 2² + 2³ +.....+2⁹⁸)

A = ( 2 - 2 ) +  ( 2² - 2² ) + (2³ - 2³).....+(2⁹⁸ - 2⁹⁸) + 2⁹⁹ - 1

A = 0 + 0 + 0 +.....+0  + 2⁹⁹ - 1

A = 2⁹⁹ - 1

So sánh : 

2⁹⁹ - 1 và 5 . 2⁹⁸

2⁹⁹ - 1 < 5 . 2⁹⁸

( Biết hay sai thì chịu nhe hehe phần so sánh tui 

1/51+1/52+....+1/99<1/2

$\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}=\frac{2}{3.5}+\frac{2}{5.7}+$\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}$

=$\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{11}-\frac{1}{13}$

=$\frac{1}{3}-\frac{1}{13}=\frac{10}{39}$

Vậy....

\(S=\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}\)

\(S=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\)

\(S=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\)

\(S=\dfrac{1}{3}-\dfrac{1}{13}\)

\(S=\dfrac{13}{39}-\dfrac{3}{39}\)

\(S=\dfrac{10}{39}\)

Vậy \(S=\dfrac{10}{39}\)

2/15 - 2/35 - 2/63 - 2/99 = 4 / 165

k minh di

2/15- 2/35 -2/63- 2/99 

= 2/3x5 - 2/5x7- 2/7x9 - 2/9x11

=(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)

=1/3-1/11=8/33

k nha

\(\frac{2}{15}-\frac{2}{35}-\frac{2}{63}-\frac{2}{99}=\frac{4}{165}\)

k mk nha !