\(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

= \(\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}\)

=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

=\(\frac{1}{3}-\frac{1}{7}\)

=\(\frac{4}{21}\)

1/5 + 1/5  - 1/10 + 1/10 - 1/20 + 1/20 - 1/40 + ... + 1/640 - 1/1280

= 1/5 + 1/5 - 1/1280 = 511/1280

ok bạn

1/5+1/10+1/20+...+1/1280

=1/1x5+1/

B=51​+101​+201​+401​+...+12801​

�=1⋅15+12⋅15+14⋅15+18⋅15+...+1256⋅15B=1⋅51​+21​⋅51​+41​⋅51​+81​⋅51​+...+2561​⋅51​

�=15⋅(1+12+14+18+...+1256)B=51​⋅(1+21​+41​+81​+...+2561​)

Đặt �=1+12+14+18+...+1256A=1+21​+41​+81​+...+2561​

⇒2�=2+1+12+14+...+1128⇒2A=2+1+21​+41​+...+1281​

⇒2�−�=2−1256⇒2A−A=2−2561​

�=2−1256A=2−2561​

Thay A vào B

có: �=15.(2−1256)=15⋅511256=5111280B=51​.(2−2561​)=51​⋅256511​=1280511​
 

\(A=\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{20}+\dfrac{1}{40}+\dfrac{1}{80}+\dfrac{1}{160}\\ A=\dfrac{35}{160}+\dfrac{16}{160}+\dfrac{8}{160}+\dfrac{4}{160}+\dfrac{2}{160}+\dfrac{1}{160}\\ A=\dfrac{66}{160}\\ A=\dfrac{33}{80}.\)

e cam on ah !

`1/5 + 1/10 + 1/20+1/40+1/80 + 1/160=A`

`<=> (32+16+8+4+2+1)/160=A`

`<=> 63/160=A`

bfvcf

= 51/128

=51/128 ha 

~HT~