Thuc hien cac phep tinh mot cach hop li nhat:
1 + \(\frac{1}{2}\)x (1 + 2) +\(\frac{1}{3}\)x (1 + 2 + 3) + \(\frac{1}{4}\)x (1 + 2 + 3 + 4) +......+\(\frac{1}{20}\) x (1 + 2 +...+ 20)
Giải chi tiết hộ mình nha!!!!!!!!
bai: Thuc hien phep tinh bang cach hop ly nhat:
a) \((\frac{1}{5}-\frac{1}{4})^2\)
b) \((\frac{5}{3}+\frac{1}{2}):\frac{-13}{5}+1\frac{5}{6}\)
c) \((\frac{3}{17})^4.(\frac{-17}{6})^4\)
a, \(\left(\frac{1}{5}-\frac{1}{4}\right)^2=\left(\frac{-1}{20}\right)^2=\frac{1}{400}\)
b, \(\left(\frac{5}{3}+\frac{1}{2}\right):\frac{-13}{5}+1\frac{5}{6}\)
=> \(\frac{13}{6}:\frac{-13}{5}+\frac{11}{6}\)
=> \(\frac{13}{6}.\frac{5}{-13}+\frac{11}{6}\)
=> \(\frac{-5}{6}+\frac{11}{6}=\frac{6}{6}=1\)
c, \(\left(\frac{3}{17}\right)^4.\left(\frac{-17}{6}\right)^4\)
=> \(\left(\frac{3}{17}.\frac{-17}{6}\right)^4=\left(\frac{-1}{2}\right)^4=\frac{1}{16}\)
a) \(\left(\frac{1}{5}-\frac{1}{4}\right)^2=\left(-\frac{1}{20}\right)^2=\frac{1}{400}.\)
b) \(\left(\frac{5}{3}+\frac{1}{2}\right):-\frac{13}{5}+1\frac{5}{6}\)
= \(\frac{13}{6}:\left(-\frac{13}{5}\right)+\frac{11}{6}\)
= \(\left(-\frac{5}{6}\right)+\frac{11}{6}\)
= \(1.\)
c) \(\left(\frac{3}{17}\right)^4.\left(-\frac{17}{6}\right)^4\)
= \(\left[\frac{3}{17}.\left(-\frac{17}{6}\right)\right]^4\)
= \(\left(-\frac{1}{2}\right)^4=\frac{1}{16}.\)
Chúc bạn học tốt!
Thuc hien phep tinh
1) \(\frac{1}{x+2}+\frac{3}{x^2-4}+\frac{x-14}{\left(x^2+4x+4\right).\left(x-2\right)}\)
2) \(\frac{x+1}{x-3}-\frac{1-x}{x+3}-\frac{2x.\left(1-x\right)}{9-x^2}\)
thuc hien phep tinh :
\(\frac{1}{x-1}-\frac{x^3-x}{x^2+1}\left(\frac{1}{x^2-2x+1}+\frac{1}{1-x^2}\right)\)
1) thuc hien phep tinh:
\(\frac{4}{x+2}+\frac{2}{x-2}+\frac{5x-6}{4-x}\)
Ta có :\(\frac{4}{x+2}+\frac{2}{x-2}+\frac{5x-6}{4-x}\)
\(=\frac{4\left(x-2\right)\left(4-x\right)}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}+\frac{2\left(x+2\right)\left(4-x\right)}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}\)\(+\frac{\left(5x-6\right)\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}\)
\(=\frac{24x-8x^2-32}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}+\frac{4x-2x^2+16}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}\)\(+\frac{5x^2+4x-12}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}\)
\(=\frac{24x-8x^2-32+4x-2x^2+16+5x^2+4x-12}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}\)
\(=\frac{32x-5x^2-28}{\left(x+2\right)\left(x-2\right)\left(4-x\right)}\)
Thuc hien phep tinh:
E=\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{2016}\left(1+2+...+2016\right)\)
thuc hien phep tinh sau 1 cach hop li B=(-1).(-1)^2 . (-1)^3........ (-1)^2013
\(B=\left(-1\right)\left(-1\right)^2\left(-1\right)^3...\left(-1\right)^{2013}\)
\(B=\left(-1\right)^{1+2+3+...+2013}\)
Tính tổng dãy số 1+2+3+..+2013:
+) Số các số hạng: (2013-1):1+1=2013
+) Tổng: (1+2013).2013:2=2027091.
\(B=\left(-1\right)^{2027091}=-1\)
đơn giản thôi
vì -1 mũ chắn sẽ = 1, mũ lẻ sẽ = -1
mà - 1 x -1 = 1, nên (-1)^2 x.........x (-1)^2013 sẽ được kết quả = 1
B=(-1) x 1 = -1
làm theo cách của Trần Thiên kim cũng đúng và có thể sẽ dễ hiểu hơn
THUC HIEN CAC PHEP TINH
A)3.25-16:4
B)16.17-16.14
C)20-[30-(5-1) MŨ 2]
giải chi tiết hộ cái
Thuc hien phep tinh
(x-\(\frac{1}{2}\))(2x-1)thuc hien phep tinh sau mot cach hop li
\(\frac{-1}{90}\)\(-\)\(\frac{1}{72}\)\(-\)\(\frac{1}{56}\)\(-\)\(\frac{1}{42}\)\(-\)\(\frac{1}{30}\)\(-\)\(\frac{1}{20}\)\(-\)\(\frac{1}{12}\)\(-\)\(\frac{1}{6}\)\(-\)\(\frac{1}{2}\)
Phân h các mẫu số thành tích của 2 thừa số có mối liên hệ :
90 = 10 . 9 72 = 9 . 8 56 = 8 . 7 ....
= -1/ 10 . 9 - 1 / 9 . 8 - 1 / 8 . 7 - ..... - 1 / 2 . 1
= -1/ 10 - -1/ 9 .....
Tới đây bài toán đã trở nên dễ giải hơn , bạn có thể tự làm tiếp .
ghi gium het cau ma -1/10--1/9 roi toi k cho
\(\frac{-1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(=\frac{-1}{90}-\left(\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}\right)\)
\(=\frac{-1}{90}-\left(\frac{1}{9.8}+\frac{1}{8.7}+\frac{1}{7.6}+\frac{1}{6.5}+\frac{1}{5.4}+\frac{1}{4.3}+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(=\frac{-1}{90}-\left(\frac{1}{9}-1\right)\)
\(=\frac{-1}{90}-\frac{-8}{9}\)
\(=\frac{79}{90}\)