Đặt A = \(\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+...+\frac{1}{2.2.2.....2}\)

          = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\)

=> 2A = \(2.\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\right)\)

           = \(2\times\frac{1}{2}+2\times\frac{1}{2^2}+2\times\frac{1}{2^3}+...+2\times\frac{1}{2^{50}}\)

           = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{49}}\)

 Lấy 2A - A = \(\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{49}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\right)\)

               A  = \(1+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-...-\frac{1}{2^{50}}\)

                   = \(1-\frac{1}{2^{50}}\)

Vậy  \(\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+...+\frac{1}{2.2.2.....2}\)=  \(1-\frac{1}{2^{50}}\)

a, A = 2 + 2.2 + 2.2.2 + 2.2.2.2 + ... + 2.2...2 ( 22...2 có 16 số 2)

A = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶

2A = 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷

2A - A = ( 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷) - ( 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶)

A = 2¹⁷ - 2

b, B = 1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28

1/2 x B = 1/2 + 1/6 + 1/12 + ... + 1/56

1/2 x B = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/7x8

1/2 x B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/7 - 1/8

1/2 x B = 1 - 1/8 = 7/8

B = 7/8 : 1/2

B = 7/8 x 2 = 7/4

a, A = 2 + 2.2 + 2.2.2 + 2.2.2.2 + ... + 2.2...2 ( 22...2 có 16 số 2)

A = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶

2A = 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷

2A - A = ( 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁷) - ( 2 + 2² + 2³ + 2⁴ + ... + 2¹⁶)

A = 2¹⁷ - 2

b, B = 1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28

1/2 x B = 1/2 + 1/6 + 1/12 + ... + 1/56

1/2 x B = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/7x8

1/2 x B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/7 - 1/8

1/2 x B = 1 - 1/8 = 7/8

B = 7/8 : 1/2

B = 7/8 x 2 = 7/4

=4 

tk nhé

bằng 4 đúng ko bạn ???

k nha

bảng 4 nha bn

k mik nha.bn k nha

bye bye

\(H=\frac{2\cdot2}{1\cdot5}+\frac{2\cdot2}{5\cdot9}+...+\frac{2\cdot2}{45.49}\)

\(H=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+...+\frac{4}{45\cdot49}\)

\(H=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{45}-\frac{1}{49}\)

\(H=1-\frac{1}{49}\)

\(H=\frac{48}{49}\)

\(H=\frac{2.2}{1.5}+\frac{2.2}{5.9}+\frac{2.2}{9.13}+...+\frac{2.2}{45.49}\)

\(\Rightarrow H=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{45.49}\)

\(\Rightarrow H=\frac{5-1}{1.5}+\frac{9-5}{5.9}+...+\frac{49-45}{45.49}\)

\(\Rightarrow H=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{45}-\frac{1}{49}\)

\(\Rightarrow H=1-\frac{1}{49}=\frac{48}{49}\)

đặt tử là T ta có:

2T=2(1+2+2²+2³+...+2²⁰¹⁵)

2T=2+2²+2³+...+2²⁰¹⁶

2T-T=(2+2²+2³+...+2²⁰¹⁶)-(1+2+2²+2³+...+2²⁰¹⁵)

T=2²⁰¹⁶-1

thay T vào tử của S ta được:\(S=\frac{2^{2016}-1}{1-2^{2016}}=-1\)