Question

Giúp mk nha!!

y

Answer 1

Bài 1:

Đặt \(A=1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+...+\dfrac{100}{2^{100}}\)

\(\Rightarrow2A=2+\dfrac{3}{2^2}+\dfrac{4}{2^3}+...+\dfrac{100}{2^{99}}\)

\(\Rightarrow2A-A=\left(2+\dfrac{3}{2^2}+\dfrac{4}{2^3}+...+\dfrac{100}{2^{99}}\right)-\left(1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+...+\dfrac{100}{2^{100}}\right)\)

\(\Rightarrow A=\left(2-1\right)+\dfrac{3}{2^2}+\left(\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{100}}\right)-\dfrac{100}{2^{100}}\)

\(\Rightarrow A=1+\dfrac{3}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{2^{100}}-\dfrac{100}{2^{100}}\)

\(\Rightarrow A=1+1-\dfrac{101}{2^{100}}\)

\(\Rightarrow A=2-\dfrac{101}{2^{100}}\)

Vậy \(A=2-\dfrac{101}{2^{100}}\)

Bài 2:

+) Xét \(x\ge-\dfrac{3}{4}\) ta có:

\(4x+3-x=15\)

\(\Rightarrow3x=12\)

\(\Rightarrow x=4\) ( t/m )

+) Xét \(x< \dfrac{-3}{4}\) ta có:
\(-4x-3-x=15\)

\(\Rightarrow-5x=18\)

\(\Rightarrow x=-3,6\) ( t/m )

Vậy x = 4 hoặc x = -3,6

Answer 2

Bài 1:

Đặt A = \(1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+............+\dfrac{100}{2^{100}}\)

\(\Rightarrow2A=2+\dfrac{3}{2^2}+\dfrac{4}{2^3}+\dfrac{5}{2^4}+...........+\dfrac{100}{2^{99}}\)

\(\Rightarrow2A-A=1+\dfrac{3}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+.....+\dfrac{1}{2^{99}}-\dfrac{100}{2^{100}}\)

\(\Rightarrow A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+......+\dfrac{1}{2^{99}}-\dfrac{100}{2^{100}}\)

\(\Rightarrow2A=2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+......+\dfrac{1}{2^{98}}-\dfrac{100}{2^{99}}\)

\(\Rightarrow2A-A=2-\dfrac{100}{2^{99}}-\dfrac{1}{2^{99}}+\dfrac{100}{2^{100}}\)

\(\Rightarrow A=2-\dfrac{101}{2^{99}}+\dfrac{100}{2^{100}}\)

\(\Rightarrow A=\dfrac{2^{101}}{2^{100}}-\dfrac{202}{2^{100}}+\dfrac{100}{2^{100}}\)

\(\Rightarrow A=\dfrac{2^{101}-102}{2^{100}}\)

Bài 2:

|4x+3| - x = 15 (*)

TH1: |4x+3|=4x+3 khi 4x+3 \(\ge\) 0 =>4x \(\ge\) -3 => x \(\ge\) \(-\dfrac{3}{4}\)

=> (*) có dạng:

4x+3-x=15

3x+3=15

3x=12

x=4 > \(-\dfrac{3}{4}\) ( thỏa mãn)

TH2: |4x+3|=-4x-3 khi 4x+3 <0 => 4x<-3 => x<\(-\dfrac{3}{4}\)

=> (*) có dạng:

(-4x-3)-x=15

-5x-3=15

-5x=18

x=\(-\dfrac{18}{5}\)< \(-\dfrac{3}{4}\) ( thỏa mãn )

Vậy \(x=4\) và x = \(-\dfrac{18}{5}\) thỏa mãn đề bài.