Mọi người làm giúp mk với nha
Câu 2: Tìm x biết:
b) \(\frac{x}{3}\)= \(\frac{-2}{9}\)
c) 0,5x -\(\frac{2}{3}\)x= \(\frac{7}{12}\)
Câu 5: Cho B= 3+3^2+3^3+...+3^200. Tìm số tự nhiên n, biết rằng 2B+3= 3^n
Đề khác:
Câu 5: a/ Tìm x biết:
\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+...+\(\frac{1}{x\left(x+1\right):2}\)= \(\frac{2013}{2015}\)
b/ Tính nhanh tổng sau: A= \(\frac{1}{10}\)+\(\frac{1}{15}\)+\(\frac{1}{21}\)+\(\frac{1}{28}\)+\(\frac{1}{36}\)+\(\frac{1}{45}\)+\(\frac{1}{55}\)
Câu 2 :
b) \(\frac{x}{3}=\frac{-2}{9}\)
=> x = \(\frac{-2}{9}.3\) = \(\frac{-2}{3}\)
c) \(0,5x-\frac{2}{3}x=\frac{7}{12}\)
=> \(\frac{1}{2}x-\frac{2}{3}x=\frac{7}{12}\)
=> \(-\frac{1}{6}\)x = \(\frac{7}{12}\)
=> x = \(\frac{7}{12}:\frac{-1}{6}\)
=> x =\(\frac{-7}{2}\)
Đề 1 câu 5 :
\(3B=3^2+3^3+3^4+...+3^{201}\)
\(\Rightarrow2B=3B-B=3^{201}-3\)
\(\Rightarrow2B+3=\left(3^{201}-3\right)+3=3^{201}\)
Do đó n = 201
Đề 2 câu 5 phần a)
Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}\)
thì \(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{x\left(x+1\right)}\)
; \(\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\)
; \(\frac{1}{2}A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}\)
; \(\frac{1}{2}A=\frac{1}{2}-\frac{1}{x+1}\)
Do đó \(A=\frac{\frac{1}{2}-\frac{1}{x+1}}{\frac{1}{2}}=\frac{2013}{2015}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{4030}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2013}{4030}=\frac{1}{2015}\) => x + 1 = 2015 => x = 2014
Vậy x = 2014
Đề 2 bài 5 câu b)
\(\frac{1}{2}A=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{110}\)
; \(\frac{1}{2}A=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{10.11}\)
; \(\frac{1}{2}A=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{10}-\frac{1}{11}\)
; \(\frac{1}{2}A=\frac{1}{4}-\frac{1}{11}=\frac{7}{44}\)
; \(A=\frac{7}{44}:\frac{1}{2}=\frac{7}{22}\)