Question

C=\(\frac{3}{3.5}\)+\(\frac{3}{5.7}\)+\(\frac{3}{7.9}\)+...+\(\frac{3}{47.49}\)

NHANH LEN NHE MINH CAN GAP LAM AI DUNG MINH TICH CHO !

Answer 1

\(C=\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{3}{47\cdot49}\)

\(\Rightarrow\frac{2}{3}C=\frac{2}{3}\cdot\left(\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{3}{47\cdot49}\right)\)

\(\Rightarrow\frac{2}{3}C=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{47\cdot49}\)

\(\Rightarrow\frac{2}{3}C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{47}-\frac{1}{49}\)

\(\Rightarrow\frac{2}{3}C=\frac{1}{3}-\frac{1}{49}\)

\(\Rightarrow\frac{2}{3}C=\frac{46}{147}\)

\(\Rightarrow C=\frac{46}{147}:\frac{2}{3}\)

\(\Rightarrow C=\frac{23}{49}\)

Answer 2

3/3.5+3/5.7+3/7.9+.....+3/47.49

=1-1/5+1/5-1/7+...+1/47-1/49

=1-1/49

=48/49

Answer 3

C = 3/2 . (2/3.5 + 2/5.7 + 2/7.9 + ... + 2/47.49)

C = 3/2 . (1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/47 - 1/49)

C = 3/2 . (1/3 - 1/49) = 3/2 . 46/147 = 23/49

Chúc bn HỌC TỐT nhá!!!!

Answer 4

C=3  +  3  +  3  +…+  3

   3.5    5.7   7.9      47.49

=3  -   3  +  3  -  3  +  3  -  3  +…+  3  -  3

 3       5      5     7      7      9         47     49

=3.(1-  1  +  1  -  1  +  1  -  1  +…+  1  -  1 )

            5     5      7      7     9          47    49

=3.  1   =  3

     49      49

Answer 5

C=3/2 . (2/3.5 + 2/5.7 + 2/7.9 +...+ 2/47.49)

C=3/2 . (1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 +...+ 1/47 -1/49)

C=3/2 . (1/3 - 1/49)

C=3/2 . 46/147

C=23/49