Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
A = \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2015}}\)
2A = \(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\)
2A - A =\(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\)\(-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\right)\)
A = \(2-\frac{1}{2^{2015}}\)
a) \(A=1+2+2^2+...+2^{80}\)
\(2A=2+2^2+2^3+...+2^{81}\)
\(2A-A=2+2^2+2^3+...+2^{81}-1-2-2^2-...-2^{80}\)
\(A=2^{81}-1\)
Nên A + 1 là:
\(A+1=2^{81}-1+1=2^{81}\)
b) \(B=1+3+3^2+...+3^{99}\)
\(3B=3+3^2+3^3+...+3^{100}\)
\(3B-B=3+3^2+3^3+...+3^{100}-1-3-3^2-...-3^{99}\)
\(2B=3^{100}-1\)
Nên 2B + 1 là:
\(2B+1=3^{100}-1+1=3^{100}\)
2)
a) \(2^x\cdot\left(1+2+2^2+...+2^{2015}\right)+1=2^{2016}\)
Gọi:
\(A=1+2+2^2+...+2^{2015}\)
\(2A=2+2^2+2^3+...+2^{2016}\)
\(A=2^{2016}-1\)
Ta có:
\(2^x\cdot\left(2^{2016}-1\right)+1=2^{2016}\)
\(\Rightarrow2^x\cdot\left(2^{2016}-1\right)=2^{2016}-1\)
\(\Rightarrow2^x=\dfrac{2^{2016}-1}{2^{2016}-1}=1\)
\(\Rightarrow2^x=2^0\)
\(\Rightarrow x=0\)
b) \(8^x-1=1+2+2^2+...+2^{2015}\)
Gọi: \(B=1+2+2^2+...+2^{2015}\)
\(2B=2+2^2+2^3+...+2^{2016}\)
\(B=2^{2016}-1\)
Ta có:
\(8^x-1=2^{2016}-1\)
\(\Rightarrow\left(2^3\right)^x-1=2^{2016}-1\)
\(\Rightarrow2^{3x}-1=2^{2016}-1\)
\(\Rightarrow2^{3x}=2^{2016}\)
\(\Rightarrow3x=2016\)
\(\Rightarrow x=\dfrac{2016}{3}\)
\(\Rightarrow x=672\)
\(\left(a\right)\frac{3}{7}-\left(\frac{-2}{7}\right)=\frac{3}{7}+\frac{2}{7}=\frac{5}{7}\)
\(\left(b\right)\frac{-13}{11}+\frac{6}{22}-\frac{36}{33}=\frac{-39}{33}+\frac{9}{33}-\frac{36}{33}=\frac{-66}{33}=-2\)
\(a,\frac{3}{7}-\frac{-2}{7}=\frac{3-\left(-2\right)}{7}=\frac{3+2}{7}=\frac{5}{7}\)
\(b,-\frac{13}{11}+\frac{6}{22}-\frac{36}{33}=-\frac{13}{11}+\frac{3}{11}-\frac{12}{11}=\frac{-13+3-12}{11}=-\frac{22}{11}=-2\)
\(c,-\frac{6}{17}-\frac{5}{-12}+\frac{3}{81}=-\frac{6}{17}+\frac{5}{12}+\frac{1}{27}=\frac{-6.27.12+5.17.27+17.12}{17.12.27}=\frac{185}{1836}\)
\(\frac{2}{70}-\frac{9}{-24}+\frac{-5}{42}=\frac{1}{35}+\frac{3}{8}-\frac{5}{42}=\frac{1.24+105.3-5.20}{840}=\frac{239}{840}\)
ko đấy. đằng này tớ chưa học . help
tinh
1-2-3-4 - ........ - 99 +100
Tính các tổng sau:
1, S=1-2+3_4+..+25-26
S =-1+3-5+7-...-53+55 ( có 28 số hạng )
= (-1+3)+(-5+7)+...+(-53+55) ( có 28:2=14 nhóm )
= 2+2+...+2
= 2 . 14
= 28