\(A=1+2+4+8+16+32+...+32768\)

\(A=1+2+2^2+2^3+2^4+2^5+...+2^{15}\)

\(A=2^{17}-1\)

Mình chỉ giải tóm tát thôi

~~~~~~~~~~~ai đi ngang qua nhớ để lại k ~~~~~~~~~~~~~

 ~~~~~~~~~~~~ Chúc bạn sớm kiếm được nhiều điểm hỏi đáp ~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~ Và chúc các bạn trả lời câu hỏi này kiếm được nhiều k hơn ~~~~~~~~~~~~

Khó quá

1/2 + 1/4 + 1/8 +1/16 + 1/32 + 1/64 + 1/128 

= 2 . ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 )

= 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 - 1/128 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128  ( Rồi giản ước )

= 1

A =1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

A = 64/128 + 32/128 + 16/128 + 8/128 + 4/128 + 2/128 + 1/128 

A = 217/218 tick đúng nha

\(A=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)

\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)

\(A-\frac{1}{2}A=\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{128}-\frac{1}{128}\right)+\left(\frac{1}{2}-\frac{1}{256}\right)\)

\(A=\left(\frac{1}{2}-\frac{1}{256}\right)\times2=1-\frac{1}{128}=\frac{127}{128}\)

Tính A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

=1-1/2+1/2-1/4+1/4-1/8+ ... +1/64-1/128

=127/128

TICK

đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{256}\)

=> A=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+....+\frac{1}{2^8}\)

=> 2A=\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+....+\frac{1}{2^7}\)

=> 2A-A=\(\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^8}\right)\)

=> A=\(1-\frac{1}{2^8}\)

2A=1+1/2+1/4+1/8+1/16+1/32+1/64

2A-A=(1+1/2+1/4+1/8+1/16+1/32+1/64)-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)

A=1-1/128

A=127/128

A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

suy ra: 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

2A - A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 - 1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128

A = 1 - 1/128 = 127/128

hok tốt

Dây nè nhớ nghe                                                                                                                                                                                =  1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128                                                                                                                   =1-1/128                                                                                                                                                                                                                  = 127/128

1/128+2/128+4/128+8/128+16/128+32/128+64/128=127/128

 k di

óc chó

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)đề là như vậy mới đúng

=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}+\frac{1}{64}+\frac{1}{128}\)

=\(1-\frac{1}{128}=\frac{127}{128}\)

Ta có: \(\frac{2.4+2.4.8+4.8.16+8.16.32}{3.4+2.6.8+4.12.16+8.24.32}\)

\(=\frac{4\left(2+2.8+8.16+2.16.32\right)}{4\left(3+3.8+12.16+2.24.32\right)}\)

\(=\frac{2+2.8+8.16+2.16.32}{3+3.8+12.16+2.24.32}\)

\(=\frac{2\left(1+8+64+16.32\right)}{3\left(1+8+64+16.32\right)}=\frac{2}{3}\)

Đề sai nha bạn mình sửa luôn

\(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{1+x}{\left(1-x\right)\left(1+x\right)}+\dfrac{1-x}{\left(1-x\right)\left(1+x\right)}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{1+x+1-x}{\left(1-x\right)\left(1+x\right)}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{2\left(1+x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\dfrac{2\left(1-x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{2+2x^2+2-2x^2}{\left(1-x^2\right)\left(1+x^2\right)}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{4\left(1+x^4\right)}{\left(1-x^4\right)\left(1+x^4\right)}+\dfrac{4\left(1-x^4\right)}{\left(1-x^4\right)\left(1+x^4\right)}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{4+4x^4+4-4x^4}{\left(1-x^4\right)\left(1+x^4\right)}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{8\left(1+x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\dfrac{8\left(1-x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{8+8x^8+8-8x^8}{\left(1-x^8\right)\left(1+x^8\right)}+\dfrac{16}{1+x^{16}}\)

\(=\dfrac{16\left(1+x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}+\dfrac{16\left(1-x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}\)

\(=\dfrac{16+16x^{16}+16-16x^{16}}{\left(1-x^{16}\right)\left(1+x^{16}\right)}\)

\(=\dfrac{32}{1-x^{32}}=VP\left(đpcm\right)\)

xin lỗi mk làm sai kết quả là 254

1+1+2+2+4+4+8+8+16+16+32+32+64+64=254

290 nha bn.