A=1+2+3+...+100
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Rút gọn
A= 2^100+2^99+2^98.....+2+1
B=3^100+3^99+3^98....+3+1
C=4^100+4^99+....+4+1
D=2^100- 2^99+....+2^2 - 2 + 1
E=3^100 - 3^99 + 3^98....- 3 +1
Thu gọn
M= 2 + 2^2 + 2^3 ....+ 2^100
Cho A =2+2^2+2^3+....2^100. Tìm số tự nhiên x sao cho A + 1 = 2x
Bài 1:
a: \(2A=2^{101}+2^{100}+...+2^2+2\)
\(\Leftrightarrow A=2^{100}-1\)
b: \(3B=3^{101}+3^{100}+...+3^2+3\)
\(\Leftrightarrow2B=3^{100}-1\)
hay \(B=\dfrac{3^{100}-1}{2}\)
c: \(4C=4^{101}+4^{100}+...+4^2+4\)
\(\Leftrightarrow3C=4^{101}-1\)
hay \(C=\dfrac{4^{101}-1}{3}\)
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Tính
A=1.(100-1)+2.(100-2)+3.(100-3)+..............+99.(100-99)
B=1.(100+1)+2.(100+2)+3.(100+3)+...........+99.(100+99)
A=1/2+2/2^2+3/2^3+...+100/2^100
B=1/3+2/3^2+3/3^2+...+100/3^100
A1+frac{3}{2^3}+frac{4}{2^4}+...+frac{100}{2^{100}}frac{A}{2}frac{1}{2}+frac{3}{2^4}+frac{4}{2^5}+....+frac{100}{2^{101}}A-frac{A}{2}left(1+frac{3}{2^3}+....+frac{100}{2^{100}}right)-left(frac{1}{2}+frac{3}{2^4}+.....+frac{100}{2^{101}}right)frac{A}{2}frac{1}{2}+frac{3}{2^3}+frac{1}{2^4}+frac{1}{2^5}+....+frac{1}{2^{100}}-frac{100}{2^{101}}frac{A}{2}frac{1}{2}+frac{1}{2^2}+frac{1}{2^3}+frac{1}{2^4}+....+frac{1}{2^{100}}-frac{1}{2^{101}}frac{A}{2}left(1-left(frac{1}{2}right)^{101}right).2-frac{10...
Đọc tiếp
\(A=1+\frac{3}{2^3}+\frac{4}{2^4}+...+\frac{100}{2^{100}}\)
\(\frac{A}{2}=\frac{1}{2}+\frac{3}{2^4}+\frac{4}{2^5}+....+\frac{100}{2^{101}}\)\(A-\frac{A}{2}=\left(1+\frac{3}{2^3}+....+\frac{100}{2^{100}}\right)-\left(\frac{1}{2}+\frac{3}{2^4}+.....+\frac{100}{2^{101}}\right)\)
\(\frac{A}{2}=\frac{1}{2}+\frac{3}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+....+\frac{1}{2^{100}}-\frac{100}{2^{101}}\)
\(\frac{A}{2}=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+....+\frac{1}{2^{100}}-\frac{1}{2^{101}}\)
\(\frac{A}{2}=\left(1-\left(\frac{1}{2}\right)^{101}\right).2-\frac{100}{2^{101}}\)
\(\frac{A}{2}=\frac{2^{101}-1}{2^{100}}-\frac{100}{2^{101}}\)
\(A=\frac{2^{101}-1}{2^{99}}-\frac{100}{2^{100}}\)
1/ Cho A dfrac{1}{3}-dfrac{2}{3^2}+dfrac{3}{3^3}-dfrac{4}{3^4}+.....+dfrac{99}{3^{99}}-dfrac{100}{3^{100}} Chứng minh A dfrac{3}{16}2/ Cho B(dfrac{1}{2^2}-1)(dfrac{1}{3^2}-1)....(dfrac{1}{100^2}-1) So sánh B và dfrac{-1}{2}
Đọc tiếp
1/ Cho A= \(\dfrac{1}{3}\)-\(\dfrac{2}{3^2}\)+\(\dfrac{3}{3^3}\)-\(\dfrac{4}{3^4}\)+.....+\(\dfrac{99}{3^{99}}\)-\(\dfrac{100}{3^{100}}\) Chứng minh A < \(\dfrac{3}{16}\)
2/ Cho B=(\(\dfrac{1}{2^2}\)-1)(\(\dfrac{1}{3^2}\)-1)....(\(\dfrac{1}{100^2}\)-1) So sánh B và \(\dfrac{-1}{2}\)
2:
\(B=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\cdot...\cdot\left(\dfrac{1}{100^2}-1\right)\)
\(=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{3}+1\right)\cdot...\cdot\left(\dfrac{1}{100}-1\right)\left(\dfrac{1}{100}+1\right)\)
\(=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\cdot...\cdot\left(\dfrac{1}{100}-1\right)\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\cdot...\cdot\left(\dfrac{1}{100}+1\right)\)
\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-99}{100}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{101}{100}\)
\(=-\dfrac{1}{100}\cdot\dfrac{101}{2}=\dfrac{-101}{200}< -\dfrac{100}{200}=-\dfrac{1}{2}\)
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Tính tổng: A=2^2 + 3^2 + 4^2 + ... + 100^2
A=2^2 + 3^2 + 4^2 + ... + 100^2
A=(2.3.4...100)+(2.3.4...100)+1
A=2(2.3.4....100)+1
A= ...
Tính tiếp, ngang đó mik chịu
Tính tổng: A=2^2 + 3^2 + 4^2 + ... + 100^2
A=2^2 + 3^2 + 4^2 + ... + 100^2
A=(2.3.4...100)+(2.3.4...100)+1
A=2(2.3.4....100)+1
A= ...
Tính tiếp, ngang đó mik chịu
Tinh
A=1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+...+100)
A = 1 + \(\frac{1}{2}\left(1+2\right)\)+ \(\frac{1}{3}\left(1+2+3\right)\)+ .... + \(\frac{1}{100}\left(1+2+3+...+100\right)\)
A = \(1+\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+...+\frac{1}{100}\cdot\frac{100.101}{2}\)
A = \(\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{101}{2}\)
A = \(\frac{2+3+4+...+101}{2}\)
A = \(\frac{\left(101+2\right).100}{2}\div2\)
A = \(5150\div2=2575\)
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A = 1 . 2 + 2 . 3 + 3 . 4 + ......... + 98 . 99 / 1 + ( 1 + 2 ) + ( 1 + 2 + 3 ) + ........... + ( 1 + 2 + 3 + ...... + 98 )
B = ( 1 / 51 . 52 ) + 1 / 52 . 53 + ...... + 1 / 100 . 101 ) : ( 1 / 1 . 2 + 1 / 2 . 3 + ........ + 1 / 99 . 100 + 1 / 100 . 101
tính a100 biết
a1-1/100=a2-2/99=a3-3/98=.........=a100-100/1
và a1+a2+a3+....+a100=10100 (TRÌNH BÀY RA ĐÚNG MÌNH TICK LUN)
THANKS