cho M=1/2-3/4+5/6-7/8+...+197/198-199/200 và N=1/51+1/52+...+1/100. Chứng minh N:M < -1,9
Những câu hỏi liên quan
Cho M= 1/2-3/4+5/6-7/8+...+197/198-199/200
N= 1/51+1/52+1/53+...+1/100
Tính N:M
Cho M=\(\frac{1}{2}-\frac{3}{4}+\frac{5}{6}-\frac{7}{8}+...+\frac{197}{198}-\frac{199}{200}\)
N=\(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{100}\)
Tính N:M
\(M=\left(1-\frac{1}{2}\right)-\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{6}\right)-....-\left(1-\frac{1}{200}\right)\)
\(M=-\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{6}-.....-\frac{1}{200}\right)=-\frac{1}{2}\left(1-\frac{1}{2}+...-\frac{1}{100}\right)\)
Xét:
\(S=1-\frac{1}{2}+....-\frac{1}{100}.S=\left(1+\frac{1}{2}+...+\frac{1}{100}\right)-2\left(\frac{1}{2}+....+\frac{1}{100}\right)=\frac{1}{51}+...+\frac{1}{100}\)
\(\Rightarrow M=-\frac{1}{2}\left(\frac{1}{51}+....+\frac{1}{100}\right)\)
N:M=-2
Cho M= 1/2-3/4+5/6-7/8+...+197/198-199/200
và N= 1/51+1/52+...+1/100
Cho M=1/51+1/52+.....+1/100 và N=1/2-3/4+5/6-7/8+.....+197/198-199/200.
Hãy tính M:N
b) Cho M= 1/2 - 3/4 + 5/6 - 7/8 +...+ 197/198 - 199/200 và N = 1/51+1/52+1/53+...+1/100
Tính N : M
tìm N:M biết
\(M=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}-\frac{7}{8}+...+\frac{197}{198}-\frac{199}{200}\)
\(N=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)
help me
Cho M =1/2-3/4+5/6 -7/8+...+197/198-199/200
Và N= 1/51+1/52+...+1/100
Tính M:N
cho M=1/2-3/4+5/6-7/8+...+197/198-199/200 N=1/51+1/52+1/53+...+1/100 tính M/N
\(M=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}-\frac{7}{8}+...+\frac{197}{198}-\frac{199}{200}\)
\(=\left(1-\frac{1}{2}\right)-\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{6}\right)-\left(1-\frac{1}{8}\right)+...+\left(1-\frac{1}{198}\right)-\left(1-\frac{1}{200}\right)\)=\(=-\frac{1}{2}+\frac{1}{4}-\frac{1}{6}+\frac{1}{8}-...-\frac{1}{198}+\frac{1}{200}\)
\(=-\frac{1}{2}\left(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=-\frac{1}{2}\left[\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\right]\)
\(=-\frac{1}{2}\left[\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)\right]\)
\(=-\frac{1}{2}\left(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+...+\frac{1}{100}\right)\)
\(=-\frac{1}{2}.N\)
\(Tacó:\)
\(M:N=-\frac{1}{2}.N:N=-\frac{1}{2}\)
M=1/2-3/4+5/6-7/8+...+197/198-199/200
N=1/51+1/52+1/53+...+1/100
Tính M : N