Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}\)
Ta có:
\(\frac{1}{2^2}< \frac{1}{1\times2}\)
\(\frac{1}{3^2}< \frac{1}{2\times3}\)
\(\frac{1}{4^2}< \frac{1}{3\times4}\)
\(...\)
\(\frac{1}{10^2}< \frac{1}{9\times10}\)
\(\rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< \frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\)
\(\Rightarrow S< \frac{9}{10}\)mà \(S>0\Rightarrow\left[S\right]=0\)
a) \(3.5^2-16:2^2\)
\(=3.25-16.4\)
\(=75-64\)
\(=11\)
b) \(17.85+15.17-120\)
\(=17.\left(85+15\right)-120\)
\(=17.100-120\)
\(=1700-120\)
\(=1580\)
c) \(\left(3^{15}.4+5.3^{15}\right):3^{16}\)
\(=\left[3^{15}.\left(4+5\right)\right]:3^{16}\)
\(=\left[3^{15}.9\right]:3^{16}\)
\(=\left[3^{15}.3^2\right]:3^{16}\)
\(=3^{17}:3^{16}\)
\(=3\)
a. 3.52 - 24 : 22 = 3.52- 22 = 3.25-4= 75-4 =71
b. 17.(85+15) - 120 = 17.100-120=1700-120=1580
c. |315.(4+5)| :316= (315.9) : 316= 315.32 : 316= 317:316=3
dấu | là ngoặc vuông bn nhé
Đặt \(A=1+2+2^2+2^3+...+2^{59}+2^{60}\)
\(\Leftrightarrow\)\(2A=2+2^2+2^3+2^4+...+2^{60}+2^{61}\)
\(\Leftrightarrow\)\(2A-A=\left(2+2^2+2^3+2^4+...+2^{60}+2^{61}\right)-\left(1+2+2^2+2^3+...+2^{59}+2^{60}\right)\)
\(\Leftrightarrow\)\(A=2^{61}-1\)
Vậy \(A=2^{61}-1\)
Năm mới zui zẻ nhá ^^
Đặt A=\(1+2+2^2+2^3+...+2^{60}\)
2A=2(\(1+2+2^2+2^3+...+2^{60}\)
2A=\(2+2^2+2^3+2^4+...+2^{61}\)
2A-A=\(\left(2+2^2+2^3+2^4+...+2^{61}\right)-\left(1+2+2^2+2^3+...+2^{60}\right)\)
A=\(2^{61}-1\)
Ta có :
\(C=4+2^2+2^3+...+2^{2016}\)
\(\Rightarrow C-4=2^2+2^3+...+2^{2016}\)
\(\Rightarrow2\left(C-4\right)=2^3+2^4+...+2^{2017}\)
\(\Rightarrow2\left(C-4\right)-\left(C-4\right)=\left(2^3+2^4+...+2^{2017}\right)-\left(2^2+2^3+...+2^{2016}\right)\)
\(\Rightarrow C-4=2^{2017}-2^2\)
\(\Rightarrow C=2^{2017}\)
=> Đpcm
C= 4 + 2^2 + 2^3 + 2^4 +.....+2^2016
Đặt A= 2^2 + 2^3 + 2^4 +.....+2^2016
=>2A= 2^3 + 2^4 +2^5.....+2^2017
=>2A-A= 2^2017 - 2^2 = 2^2017 - 4
=>C= 4+A= 4+2^2017 - 4
=>C=2^2017
Vậy C là lũy thừa của 2
mong bạn sẽ tích cho mình (nếu đúng)
Mik làm 1 phần rùi bạn làm tương tự nhá :
Ta có : 3.B = 3 + 32 + 33 + ...+ 3101
=> 3.B - B = ( 3 + 32 + 33 +...+ 3101 ) - ( 1 + 3 + 32 + ...+ 3100 )
=> 2.B = 3101 - 1
=> B = \(\frac{3^{101}-1}{2}\)
Không tìm được giá trị cụ thể bạn nhá
3B=3(1+3+3^2+3^3+...+3^100)
2B=3B-B=(3+3^2+3^3+...+3^101)-(1+3+3^2+3^3+...+3^100)
=3^101-1
\(B=4+2^2+2^3+...+2^{20}\)
\(2B=8+2^3+2^4+...+2^{21}\)
\(2B-B=\left(8+2^3+2^4+...+2^{21}\right)-\left(4+2^2+2^3+...+2^{20}\right)\)
\(B=8+2^{21}-\left(4+2^2\right)=2^{21}\)
\(A=2+2^2+2^3+2^4+........+2^{600}\)
\(\Rightarrow2A=2^2+2^3+2^4+2^5+..........+2^{601}\)
\(\Rightarrow2A-A=2^{601}-2\)
\(\Rightarrow A=2^{601}-2\)
\(A=2^2+2^3+2^4+...+2^{600}\)
\(\Rightarrow2A=2^3+2^4+2^5+...+2^{601}\)
\(2A-A=\left(2^3+2^4+2^5+...+2^{601}\right)-\left(2^2+2^3+...+2^{600}\right)\)
\(\Leftrightarrow2A-A=A=2^{601}-2^2\)