Thực hiện phép tính :
\(D=\frac{2.2018}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+2018}}\)
Những câu hỏi liên quan
D=\(\frac{2.2018}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+2018}}\)
Thực hiện phép tính:\(\left(1-\frac{1}{2018}\right).\left(1-\frac{2}{2018}\right).\left(1-\frac{3}{2018}\right)...\left(1-\frac{2020}{2018}\right)\)
Thực hiện phép tính : \(\left(1\frac{1}{1+2}\right).\left(1\frac{1}{1+2+3}\right)...\left(1\frac{1}{1+2+3+...+2018}\right)\)
Thực hiện phép tính
\(\left(1-\frac{1}{1+2}\right).\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+2018}\right)\)
Thực hiện các phép tính sau một cách hợp lí:
\(D=\frac{2.2012}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.....+\frac{1}{1+2+3+......2012}}\)
Co quy luat nay ne em: 1+2=3=2.3:2; 1+2+3=6=3.4:2;...;1+2+3+...+2012=2012.2013:2
Suy ra ta co:
Mau so cua D=1 + 1/(2.3:2) + 1/(3.4:2) + 1/(4.5:2) + .... + 1/(2012.2013:2)
=1 + 2/2.3 + 2/3.4 + 2/4.5 + .... + 2/2012.2013
= 2.[1/2 + 1/2.3 + 1/3.4 + 1/4.5 + .... + 1/2012.2013]
=2.[1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ..... + 1/2012.2013]
=2.[1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +....+1/2012 - 1/2013
=2[1 - 1/2013]
=2.2012/2013
Vay D= 2.2012 / (2.2012:2013)=2013
Đúng 0
Bình luận (0)
thực hiện phép tính:
\(\left(1\frac{1}{1+2}\right).\left(1\frac{1}{1+2+3}\right).....\left(1\frac{1}{1+2+3+...+2018}\right)\)
Thực hiện phép tính:
\(\left(1-\frac{1}{1+2}\right).\left(1-\frac{1}{1+2+3}\right).....\left(1-\frac{1}{1+...+2018}\right)\)
( 1 - \(\frac{1}{1+2}\)) . ( 1 - \(\frac{1}{1+2+3}\)) ... ( 1 - \(\frac{1}{1+2+3+...+2018}\) )
Thực hiện phép tính trên
Thực hiện phép tính
( 1 - \(\frac{1}{1+2}\)) . ( 1 - \(\frac{1}{1+2+3}\)) ... ( 1 - \(\frac{1}{1+2+3+...+2018}\))
\(\left(1-\frac{1}{1+2}\right).\left(1-\frac{1}{1+2+3}\right).....\left(1-\frac{1}{1+2+3+.....+2018}\right)\)
\(=\left(1-\frac{1}{\frac{2.3}{2}}\right).\left(1-\frac{1}{\frac{3.4}{2}}\right).......\left(1-\frac{1}{\frac{2018.2019}{2}}\right)\)
\(=\left(1-\frac{2}{2.3}\right).\left(1-\frac{2}{3.4}\right).......\left(1-\frac{2}{2018.2019}\right)\)
\(=\left(1-\frac{1}{3}\right).\left(1-\frac{5}{6}\right).......\left(1-\frac{1}{2037171}\right)\)
\(=\frac{2}{3}.\frac{5}{6}......\frac{2037170}{2037171}\)
\(=\frac{4}{6}.\frac{10}{12}.......\frac{4074340}{4074342}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}......\frac{2017.2020}{2018.2019}\)
\(=\frac{1.2......2017}{2.3.....2018}.\frac{4.5......2020}{3.4......2019}=\frac{1}{2018}.\frac{2020}{3}=\frac{1010}{3027}\)
Đúng 0
Bình luận (0)