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đặt B = 100/3 + 100/3^2 + 100/3^3 + 100/3^4
B = 100 x ( 1/3 + 1/3^2 +1/3^3 +1/3^4 )
đặt A = 1/3 + 1/3^2 + 1/3^3 + 1/3^4
3A = 1 + 1/3 + 1/3^2 + 1/3^3
3A - A = 1 - 1/3^4
2A = 81/81 - 1/81 = 80/81
A = 80/81 : 2 = 40/81
thay A vào B ta có B= 100 x 40/81 = 4000/81
vậy B = 4000 /81
chúc bạn hok tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
(10099+9999)100=10099x100+9999x100
(100100+99100)99=100100x99+99100x99
Vì100100x99+99100x99=10099x100+9999x100
=>M=N
Các bạn nhớ nha !!!
![](https://rs.olm.vn/images/avt/0.png?1311)
Áp dụng a /b > 1 => a/b > a+m/b+m (a;b;m thuộc N*)
Ta có:
\(\frac{100^{10}-1}{100^{10}-3}>\frac{100^{100}-1+2}{100^{10}-3+2}\)
\(>\frac{100^{100}+1}{100^{10}-1}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = (\(\dfrac{1}{100}\) - 12).(\(\dfrac{1}{100}\) - \(\dfrac{1}{2^2}\)).(\(\dfrac{1}{100}\) - \(\dfrac{1}{3^2}\))...(\(\dfrac{1}{100}\) - \(\dfrac{1}{20^2}\))
A = (\(\dfrac{1}{10^2}\) - 12).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{2^2}\)).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{3^2}\))..(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{10^2}\))....(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{20^2}\))
A = (\(\dfrac{1}{10^2}\) - 12).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{2^2}\)).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{3^2}\))...0.(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{20^2}\))
A = 0
![](https://rs.olm.vn/images/avt/0.png?1311)
A=-1++(-1)+..+-(1) có 50 số -1
=>A=-1x50=-50
B=(1-2-3+4)+(5-6-7+8)+...+(97-98-99+100)
B=0+0+0+..+0
B=0
C=2^100-(2^99+2^98+...+1)
C=2^100-(2^100-1)
C=1
100 + 100 + 100+...........+100=100^9?
sai rồi nhé
100+100+...+100=1009 = 1000000000000000000