Question

Tính hợp lý: 

a. S= 1+ 1/2 + 1/2^2 + 1/2^3 +...+ 1/2^100

b. D = 1/3 + 1/3^2 + 1/3^3 + 1/3^4 +...+ 1/3^300

 

Answer 1

a)\(2S=2\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)\)

\(2S=2+1+...+\frac{1}{2^{99}}\)

\(2S-S=\left(2+1+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)\)

\(S=2-\frac{1}{2^{100}}\)

phần b tương tự

Answer 2

a. S=1+1/2+1/2^2+1/2^3+...+1/2^100

2S=2+1+1/2+1/2^2+...+1/2^99

2S-S=(2+1+1/2+1/2^2+...+1/2^99)-(1+1/2+1/2^2+1/2^3+...+1/2^100)

S=2-1/2^100

S=2^101-1/2^100

Answer 3

b. D=1/3+1/3^2+1/3^3+1/3^4+...+1/3^300

3D=1+1/3+1/3^2+1/3^3+...+1/3^299

3D-D=(1+1/3+1/3^2+1/3^3+...+1/3^299)-(1/3+1/3^2+1/3^3+1/3^4+...+1/3^300)

2D=1-1/3^300

D=1-1/3^300/2

Answer 4

a. S=1+1/2+1/2^2+1/2^3+...+1/2^100

2S=2+1+1/2+1/2^2+...+1/2^99

2S-S=(2+1+1/2+1/2^2+...+1/2^99)-(1+1/2+1/2^2+1/2^3+...+1/2^100)

S=2-1/2^100

S=2^101-1/2^100