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\(D=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+......+\frac{1}{29.31}\)
\(\Rightarrow D=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+......+\frac{1}{2}.\left(\frac{1}{29}-\frac{1}{31}\right)\)
\(\Rightarrow D=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{31}\right)\)
\(\Rightarrow D=\frac{1}{2}.\frac{28}{93}=\frac{14}{94}\)
NHỚ LIKE CHO MÌNH NHA ^_^
A bn lướt xuống dưới mà xem cách làm
nhưng của bn là cho 3 ra ngoài nha
TA CÓ:
Đặt C = \(\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{29.31}\)
\(\Rightarrow\frac{2}{5}C=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{29.31}\)
\(\Rightarrow\frac{2}{5}C=\frac{1}{3}-\frac{1}{31}=\frac{28}{93}\)
\(\Rightarrow C=\frac{28}{93}:\frac{2}{5}=\frac{70}{93}\)
Tương tự, đặt \(D=\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{29.31}\)
Mà \(D=C\)
\(\Rightarrow D=\frac{70}{93}\)
Đặt \(B=\frac{3}{2.3}+\frac{3}{3.4}+.....+\frac{3}{15.16}\)
\(\Rightarrow\frac{1}{3}B=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{15.16}\)
\(\Rightarrow\frac{1}{3}B=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}\)
\(\Rightarrow B=\frac{7}{16}:\frac{1}{3}=\frac{21}{16}\)
Nên \(\frac{5}{3.5}+...+\frac{5}{29.31}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{29.31}+\frac{3}{2.3}+..+\frac{3}{15.16}\)
\(\Rightarrow C+D+B=C.2+B=\frac{140}{93}+\frac{21}{16}=2,81\)
\(37.9-\left(-895\right)\)
\(=333+895\)
\(=1228\)
k mik nha
thank you
2.
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{9}\right)+...+\frac{1}{2}.\left(\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{15}{93}\)
\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{15}{93}:\frac{1}{2}\)
\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)
\(\Rightarrow\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)
\(\Rightarrow\frac{1}{2x+3}=\frac{1}{93}\)
\(\Rightarrow\)2x + 3 = 93
\(\Rightarrow\)2x = 93 - 3
\(\Rightarrow\)2x = 90
\(\Rightarrow\)x = 90 : 2 = 45
\(H=\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{33.37}\)
= \(\frac{3}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{33}-\frac{1}{37}\right)\)
= \(\frac{3}{4}\left(1-\frac{1}{37}\right)\)
= \(\frac{3}{4}.\frac{36}{37}=\frac{27}{37}\)
\(P=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{29.31}\)
=> \(2P=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{29.31}\)
\(=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{31-29}{29.31}\)
\(=\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{29}-\frac{1}{31}\right)\)
\(=1-\frac{1}{31}=\frac{30}{31}\)
=> \(P=\frac{30}{31}:2=\frac{15}{31}\)
Nếu đề là tính thì bạn làm như sau nhé :
\(P=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{29.31}\)
\(\Rightarrow2P=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{29.31}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{29}-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{30}{31}\)
\(\Rightarrow P=\frac{30}{31}\div2=\frac{15}{31}\)
BÀi này dễ thôi bạn ạ
N=3(1/5.7+1/7.9+.........+1/197.199)
N=3/2( 1/5-1/7+1/7-1/9+1/9-..........+1/197-1/199)
N=3/2(1/5-1/199)
N=3/2.194/995
N=291/995
k đúng cho mình nhé
N=3.1/2.(1/5-1/7+1/7-1/9+1/9-1/11+...+1/197-1/199)
N=3.1/2.(1/5-1/99)
N=3.1/2.94/495
N=3.47/495
N=47/165
dùng chức năng sicg matrên máy tính cầm tay
ct : \(\frac{3}{\left(2x+1\right)\left(2x+3\right)}\)
chạy từ 1 đến 14
=> đáp án = \(\frac{14}{31}\)
ko tính từng bước cơ bạn ạ