\(\frac{1}{5}+\frac{4}{10}+...+\frac{81}{45}=\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+...+\frac{9}{5}=\frac{1+2+3+...+9}{5}=\frac{45}{5}=9\)

1/5 + 4/10 + 9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45

=1/5 + 2/5 + 3/5 + 4/5 + 5/5 + 6/5 + 7/5 + 8/5 + 9/5

=45/5 = 9

#)Giải :

\(\frac{1}{15}+\frac{4}{30}+\frac{9}{45}+\frac{16}{60}+...+\frac{81}{135}=\frac{1}{15}+\frac{2}{15}+\frac{3}{15}+...+\frac{9}{15}=\frac{45}{15}=3\)

Dễ ẹc ak :v rút gọn là ra

=(\(\frac{1}{15}\)+\(\frac{4}{30}\)+\(\frac{16}{60}\)+\(\frac{64}{120}\))+(\(\frac{9}{45}\)+\(\frac{36}{90}\))+(\(\frac{25}{75}\)+\(\frac{81}{135}\))

=(\(\frac{8}{120}\)+\(\frac{16}{120}\)+\(\frac{32}{120}\)+\(\frac{64}{120}\))+(\(\frac{18}{90}\)+\(\frac{36}{90}\))+\(\frac{14}{15}\).

=1+\(\frac{3}{5}\)+\(\frac{14}{15}\).

=\(\frac{8}{5}\)+\(\frac{14}{15}\).

=\(\frac{15}{38}\)

=\(-\frac{11}{20}\)

a) = \(\frac{7}{2}\)

b) = \(\frac{643}{64}\)

c) = 0

1/10+4/20+9/30+16/40+25/50+36/60+49/70+64/80+81/90

=1/10+2/10+3/10+4/10+5/10+6/10+7/10+8/10+9/10

=1+2+3+4+5+6+7+8+9/10

=45/10 (tự rút gọn)

Rút gọn các phân số ta có :

 1/10 + 2/10 + 3/10 + 4/10 + 5/10 + 6/10 + 7/10 + 8/10 + 9/10

= ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) / 10 

= 45/10 = 4,5 

a)     5/30+15/90+25/150+35/210+45/270

       =1/6+1/6+1/6+1/6+1/6

       =1/6 x 5

       =5/6

b)     1/2+1/6+1/12+1/20+....+1/56

        =1/1x2+1/2x3+1/3x4+1/4x5+.....1/7x8

        =1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.......-1/7+1/7-1/8

        =1/1-1/8

         =7/8

c)     mình chịu

thank you bn nhìu nha

\(\frac{1}{2^2}+\frac{1}{4^2}+.....+\frac{1}{100^2}=\frac{1}{2^2}\cdot\left(1+\frac{1}{2^2}+...+\frac{1}{50^2}\right)

\(có\)  \(\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}\approx1,4\)

\(mà\)  \(\frac{1}{2}=1,5\)

\(=>\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}<\frac{1}{2}\)

\(\frac{1}{4}+\frac{1}{16}+...+\frac{1}{196}\)\(<\frac{1}{2^2-1}+\frac{1}{4^2-1}+\frac{1}{6^2-1}+...+\frac{1}{14^2-1}\)

\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{15}\right)<\frac{1}{2}\) \(\left(đpcm\right)\)

B=1/2²+1/4²+...+1/14²

4B=1+1/2²+...+1/7² nhỏ hơn hoặc bằng 1+1/1.2+1/2.3+...+1/6.7 = 2-1/7=13/7

B nhỏ hỏn hoặc bằng 13/28 nhỏ hơn 1/2

vậy B nhỏ hơn 1/2