Question

Tính tổng : \(S1=\frac{15}{1.3}+\frac{15}{3.5}+\frac{15}{5.7}+......+\frac{15}{2017.2019}\)

Giúp mik với ạ !!!

 

Answer 1

Bài làm

\(S_1=\frac{15}{1.3}+\frac{15}{3.5}+\frac{15}{5.7}+...+\frac{15}{2017.2019}\)

\(S_1=15.\frac{1}{1.3}+15.\frac{1}{3.5}+15.\frac{1}{5.7}+...+15.\frac{1}{2017.2019}\)

\(S_1=15.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\right)\)

\(S_1=15.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(S_1=15.\left(1-\frac{1}{2019}\right)\)

\(S_1=15.\left(\frac{2019}{2019}-\frac{1}{2019}\right)\)

\(S_1=15.\frac{2018}{2019}\)

\(S_1=\frac{2018}{673}\)

# Chúc bạn học tốt #

Answer 2

Bài làm

Chắc zậy, không chắc nữa.

~ Sai thì thôi nha ~
# Học tốt #

Answer 3

\(S1=\frac{15}{1.3}+\frac{15}{3.5}+\frac{15}{5.7}+...+\frac{15}{2017.2019}\)

\(S1=\frac{15}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\right)\)

\(S1=\frac{15}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(S1=\frac{15}{2}.\left(1-\frac{1}{2019}\right)\)

\(S1=\frac{15}{2}.\frac{2018}{2019}\)

\(S1=\frac{5045}{673}\)

Answer 4

\(S=\frac{15}{1\cdot3}+\frac{15}{3\cdot5}+\frac{15}{5\cdot7}+...+\frac{15}{2017\cdot2019}\)

\(\Rightarrow S=\frac{15}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{2017\cdot2019}\right)\)

\(\Rightarrow S=\frac{15}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(\Rightarrow S=\frac{15}{2}\cdot\left(1-\frac{1}{2019}\right)=\frac{15}{2}\cdot\left(\frac{2019}{2019}-\frac{1}{2019}\right)\)

\(\Rightarrow S=\frac{15}{2}\cdot\frac{2018}{2019}=\frac{15\cdot2018}{2\cdot2019}=\frac{2\cdot1009\cdot3\cdot5}{2\cdot673\cdot3}\)

\(\Rightarrow S=\frac{1009\cdot5}{673}=\frac{5045}{673}\)

Answer 5

\(S_1=\frac{15}{1\cdot3}+\frac{15}{3\cdot5}+\frac{15}{5\cdot7}+...+\frac{15}{2017\cdot2019}\)

\(S_1=\frac{15}{2}\left[\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{2017\cdot2019}\right]\)

\(S_1=\frac{15}{2}\left[1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2017}-\frac{1}{2019}\right]\)

\(S_1=\frac{15}{2}\left[1-\frac{1}{2019}\right]\)

\(S_1=\frac{15}{2}\cdot\frac{2018}{2019}=\frac{5}{1}\cdot\frac{1009}{673}=\frac{5045}{673}\)

Answer 6

\(S=\frac{15}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2017.2019}\right)\)

\(S=\frac{15}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(S=\frac{15}{2}.\frac{2018}{2019}\)
S=\(\frac{5054}{673}\)