A=\(\dfrac{18360}{151}\)

B=\(\dfrac{1510}{3}\)

*Giải bằng casio

ghi phép tính đầy đủ ạ

mk biết ai bik làm.toán bk làm đó

gợi ý nè:giống 1 dạng ở toán olympic ,tớ chỉ đổi số thôi VD:4nhan1-2nhan2=0

vừa chỉ cách giải,tick cho tớ nhe

21)

\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).....\left(1+\dfrac{1}{9999}\right)\\ =\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{10000}{9999}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{100.100}{99.101}\\ =\dfrac{2.3.4.....100}{1.2.3.....99}.\dfrac{2.3.4.....100}{3.4.5.....101}\\ =100.\dfrac{2}{101}\\ =\dfrac{200}{101}\)

\(\frac{1}{2}B=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}=\frac{1}{4}-\frac{1}{16}=\frac{3}{16}\)

=>\(B=\frac{3}{16}:\frac{1}{2}=\frac{3}{8}\)

\(C=\left(\frac{3}{29}-\frac{1}{5}\right)\cdot\frac{29}{3}=1-\frac{1}{5}\cdot\frac{29}{3}=1-\frac{29}{15}=-\frac{14}{15}\)

\(A=1+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}\)

\(< =>A=1+\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}\)

\(< =>2A=2+\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}\)

\(< =>2A=2+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}\)

\(< =>2A=\frac{5}{2}-\frac{1}{12}=\frac{29}{12}\)

\(< =>A=\frac{29}{12}.\frac{1}{2}=\frac{29}{24}\)

Với \(k\in N;k\ne0\) ta có :

\(\frac{1}{\left(k+1\right)\sqrt{k}+k\sqrt{\left(k+1\right)}}=\frac{1}{\sqrt{k\left(k+1\right)}\left(\sqrt{k}+\sqrt{k+1}\right)}\)

\(=\frac{\sqrt{k+1}+\sqrt{k}}{\sqrt{k\left(k+1\right)}\left(\sqrt{k+1}-\sqrt{k}\right)\left(\sqrt{k+1}+\sqrt{k}\right)}=\frac{\sqrt{k+1}-\sqrt{k}}{\sqrt{k\left(k+1\right)}}\)

\(=\frac{1}{\sqrt{k}}-\frac{1}{\sqrt{k+1}}\)

Áp dụng ta có :

\(M=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+....+\frac{1}{\sqrt{120}}-\frac{1}{\sqrt{121}}=1-\frac{1}{11}=\frac{10}{11}\)

(1+1/3)(1+1/8)(1+1/15)...(1+1/9603)=4/3 . 9/8 . 16/15 ... 9604/9603

                                                   = (2.2)/(1.3) . (3.3)/(2.4) . (4.4)/(3.5) ... (98.98)/(97.99)

                                                   =(2.2.3.3.4.4...98.98)/(1.3.2.4.3.5...97.99)

                                                   =(2.3.4...98)/(1.2.3...97) . (2.3.4..98)/(3.4.5...99)

                                                   =98/1 .2/99 =169/99 .         

đây là toán 6 thì đúng hơn

1+1/3)(1+1/8)(1+1/15)...(1+1/9603)=4/3 . 9/8 . 16/15 ... 9604/9603

                                                   = (2.2)/(1.3) . (3.3)/(2.4) . (4.4)/(3.5) ... (98.98)/(97.99)

                                                   =(2.2.3.3.4.4...98.98)/(1.3.2.4.3.5...97.99)

                                                   =(2.3.4...98)/(1.2.3...97) . (2.3.4..98)/(3.4.5...99)

                                                   =98/1 .2/99 =169/99

=28/15 x 0,25 x 3 + (8/15 - 79/60) : 47/24

= 28/15 x 0,25 x 3 + (-47/60) : 47/24

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