2: \(M=\frac13-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+\cdots-\frac{30}{3^{30}}\)

=>3M=\(1-\frac23+\frac{3}{3^2}-\frac{4}{3^3}+\cdots-\frac{30}{3^{29}}\)

=>3M+M=\(1-\frac23+\frac{3}{3^2}-\frac{4}{3^3}+\cdots-\frac{30}{3^{29}}+\frac13-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+\cdots-\frac{30}{3^{30}}\)

=>4M=\(1-\frac13+\frac{1}{3^2}-\cdots-\frac{1}{3^{29}}-\frac{30}{3^{30}}\)

Đặt \(A=-\frac13+\frac{1}{3^2}-\frac{1}{3^3}+\cdots-\frac{1}{3^{29}}\)

=>3A=-1+\(\frac13-\frac{1}{3^2}+\cdots-\frac{1}{3^{28}}\)

=>3A+A=\(-1+\frac13-\frac{1}{3^2}+\cdots-\frac{1}{3^{28}}-\frac13+\frac{1}{3^2}-\frac{1}{3^3}+\cdots-\frac{1}{3^{29}}\)

=>4A=\(-1-\frac{1}{3^{29}}=\frac{-3^{29}-1}{3^{29}}\)

=>\(A=\frac{-3^{29}-1}{4\cdot3^{29}}\)

Ta có: \(4M=1-\frac13+\frac{1}{3^2}-\cdots-\frac{1}{3^{29}}-\frac{30}{3^{30}}\)

\(=1+\frac{-3^{29}-1}{4\cdot3^{29}}-\frac{30}{3^{30}}=1+\frac{-3^{30}-3-120}{4\cdot3^{30}}=1-\frac14-\frac{123}{4\cdot3^{30}}=\frac34-\frac{123}{4\cdot3^{30}}\)

=>4M<3/4

=>M<3/16

bạn k cho mik rồi mik mới trả lời

Câu 11:

(\(\dfrac{11}{4}\). \(\dfrac{-5}{9}\) - \(\dfrac{4}{9}\).\(\dfrac{11}{4}\)).\(\dfrac{8}{33}\)

= \(\dfrac{11}{4}\).(\(\dfrac{-5}{9}\)  - \(\dfrac{4}{9}\)). \(\dfrac{8}{33}\)

= \(\dfrac{11}{4}\).(-1).\(\dfrac{8}{33}\)

= - \(\dfrac{2}{3}\)

1 + 2-3-4+5+6-7-8+9+...+28-29-30+31 + 32

= 1 + (2-3-4+5) + (6-7-8+9) + ...+(28-29-30+31) + 32

= 1 + 0+0+...+0+32

= 1+32

=33

1+2-3-4+5+6-7-8+9+...+28-29-30+31+32?

 ( 1 + 2 - 3 - 4 ) + ( 5 + 6 - 7 - 8 ) + ...... + ( 29 + 30 - 31 - 32 )

=         0             +         0            + ....+           0

= 0

1,35326087

-2/3

0

-6/29/44

-9

nha bạn

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30

21

69

78

35

27

105

-13

30

21

69

78

35

27

105

Giúp tớ với tớ cần gấp

a: \(=\dfrac{-5}{7}-\dfrac{2}{7}+\dfrac{3}{4}+\dfrac{1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)

b: \(=\dfrac{-3}{31}-\dfrac{28}{31}+\dfrac{-6}{17}-\dfrac{11}{17}+\dfrac{1}{29}-\dfrac{1}{5}=\dfrac{-24}{145}\)

18?

190:))