Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Mình làm mẫu 1 bài rùi bạn tự giải những bài còn lại nha
1, 7A = 7+7^2+7^3+....+7^2008
6A = 7A - A = (7+7^2+7^3+....+7^2008)-(1+7+7^2+....+7^2007) = 7^2008-1
=> A = (7^2008-1)/6
Tk mk nha
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(\Rightarrow7A-A=\left(7+7^2+7^3+...+7^{2008}\right)-\left(1+7+7^2+...+7^{2007}\right)\)
\(\Rightarrow6A=7^{2008}-1\)
\(\Rightarrow A=\frac{7^{2008}-1}{6}\)
a; - \(\dfrac{10}{13}\) + \(\dfrac{5}{17}\) - \(\dfrac{3}{13}\) + \(\dfrac{12}{17}\) - \(\dfrac{11}{20}\)
= - (\(\dfrac{10}{13}\) + \(\dfrac{3}{13}\)) + (\(\dfrac{5}{17}\) + \(\dfrac{12}{17}\)) - \(\dfrac{11}{20}\)
= - 1 + 1 - \(\dfrac{11}{20}\)
= 0 - \(\dfrac{11}{20}\)
= - \(\dfrac{11}{20}\)
b; \(\dfrac{3}{4}\) + \(\dfrac{-5}{6}\) - \(\dfrac{11}{-12}\)
= \(\dfrac{9}{12}\) - \(\dfrac{10}{12}\) + \(\dfrac{11}{12}\)
= \(\dfrac{10}{12}\)
= \(\dfrac{5}{6}\)
c; [13.\(\dfrac{4}{9}\) + 2.\(\dfrac{1}{9}\)] - 3.\(\dfrac{4}{9}\)
= [\(\dfrac{52}{9}\) + \(\dfrac{2}{9}\)] - \(\dfrac{4}{3}\)
= \(\dfrac{54}{9}\) - \(\dfrac{4}{3}\)
= \(\dfrac{14}{3}\)
a)\(1-2+3-4+5-6+7-8+8-9+9-10\)
=\(\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+\left(7-8\right)+\left(8-9\right)+\left(9-10\right)\)
\(=\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)\)
\(=\left(-1\right).6\)
\(=-6\)
b)\(1-2+3-4+...+99-100\)
\(=\left(1-2\right)+\left(3-4\right)+...+\left(99-100\right)\)}\(\left[\left(100-1\right):1+1\right]:2=50\)(cặp)
\(=\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)} 50 số (-1)
\(=\left(-1\right).50\)
\(=-50\)
c)\(1-3+5-7+9-11+13-15\)
\(=\left(1-3\right)+\left(5-7\right)+\left(9-11\right)+\left(13-15\right)\)
\(=\left(-2\right)+\left(-2\right)+\left(-2\right)+\left(-2\right)\)
\(=\left(-2\right).4\)
\(=-8\)
d)\(1-3+5-7+...-99+101\) (Đối với bài này, có vẻ đề sai, mình đã sửa lại rồi
\(=\left(1-3\right)+\left(5-7\right)+...+\left(97-99\right)+101\) } \(\left[\left(99-1\right):2+1\right]:2=25\)(cặp)
\(=\left(-2\right)+\left(-2\right)+\left(-2\right)+...+\left(-2\right)\) } 25 số (-2)
\(=\left(-2\right).25\)
\(=-50\)
e)\(-1-2-3-4-...-99-100\)
\(=\left(-1\right)+\left(-2\right)+\left(-3\right)+...+\left(-99\right)+\left(-100\right)\)
\(=\left[\left(-1\right)+\left(-100\right)\right]+\left[\left(-2\right)+\left(-99\right)\right]+...+\left[\left(-51\right)+\left(-50\right)\right]\) } \(\left[\left(100-1\right):1+1\right]:2=50\)(cặp) (phần này của đề bài, không thay được như (-100) hoặc (-1))
\(=\left(-100\right)+\left(-100\right)+\left(-100\right)+...+\left(-100\right)\)} 50 số (-100)
\(=\left(-100\right).50\)
\(=-5000\)
a) \(\frac{3}{5}+\frac{7}{10}+\frac{-13}{20}=\frac{12}{20}+\frac{14}{20}+\frac{-13}{20}=\frac{12+14+\left(-13\right)}{20}=\frac{13}{20}\)
b) \(\frac{1}{2}+\frac{-1}{5}+\frac{1}{4}+\frac{1}{6}=\frac{60}{120}+\frac{-24}{120}+\frac{30}{120}+\frac{20}{120}\)\(=\frac{60+\left(-24\right)+30+20}{120}=\frac{86}{120}=\frac{43}{60}\)
c) \(\frac{2}{3}+\frac{-3}{4}+\frac{5}{8}+\frac{-1}{2}\)\(=\frac{16}{24}+\frac{-18}{24}+\frac{15}{24}+\frac{-12}{24}\)\(=\frac{16+\left(-18\right)+15+\left(-12\right)}{24}=\frac{1}{24}\)
\(a)\frac{3}{5}+\frac{7}{10}+\frac{-13}{20}\)
\(\frac{3}{5}+\frac{7}{10}+\frac{-13}{20}=\frac{3.4}{5.4}+\frac{7.2}{10.2}+\frac{-12}{20}\)
\(=\frac{12}{20}+\frac{14}{20}+\frac{-13}{20}=\frac{12+14+\left(-13\right)}{20}\)
\(=\frac{13}{20}\)
\(b)\frac{1}{2}+\frac{-1}{5}+\frac{1}{4}+\frac{1}{6}\)
\(\frac{1}{2}+\frac{-1}{5}+\frac{1}{4}+\frac{1}{6}=\frac{1.30}{2.30}+\frac{-1.12}{5.12}+\frac{1.15}{4.15}+\frac{1.10}{6.10}\)
\(=\frac{30}{60}+\frac{-12}{60}+\frac{15}{60}+\frac{10}{60}=\frac{30+\left(-12\right)+15+10}{60}\)
\(=\frac{43}{60}\)
\(c)\frac{2}{3}+\frac{-3}{4}+\frac{5}{8}+\frac{-1}{2}\)
\(\frac{2}{3}+\frac{-3}{4}+\frac{5}{8}+\frac{-1}{2}=\frac{2.8}{3.8}+\frac{-3.6}{4.6}+\frac{5.3}{8.3}+\frac{-1.12}{2.12}\)
\(=\frac{16}{24}+\frac{-18}{24}+\frac{15}{24}+\frac{-12}{24}\)\(=\frac{16+\left(-18\right)+15+\left(-12\right)}{24}\)
\(=\frac{1}{24}\)
Nếu có sai chỗ nào thì báo lỗi cho tớ nhé!
Chúc cậu một buổi tối vui vẻ ~!!!!!!!!!!!
#0006