Kết quả rút gọn của B= 3 - 32 + 34 + ........ + 31999 - 32000
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
$T=3-3^2+3^3-3^4+....-3^{2000}$
$3T=3^2-3^3+3^4-3^5+...-3^{2001}$
$\Rightarrow T+3T=3-3^{2001}$
$\Rightarrow 4T=3-3^{2001}$
$\Rightarrow T=\frac{3-3^{2001}}{4}$
![](https://rs.olm.vn/images/avt/0.png?1311)
7 3 - 5 8 + 3 4 = 56 24 - 15 24 + 18 24 = 56 - 15 + 18 24 = 59 24
Đáp án cần chọn là D
![](https://rs.olm.vn/images/avt/0.png?1311)
1, Rút gọn rồi tính
a) \(\frac{4}{5}+\frac{3}{15}\)
= \(\frac{4}{5}+\frac{1}{5}\)
= \(\frac{5}{5}\)
= \(1\)
b) \(\frac{2}{3}+\frac{32}{24}\)
= \(\frac{2}{3}+\frac{4}{3}\)
= \(\frac{6}{3}\)
= \(2\)
c) \(\frac{5}{6}+\frac{15}{18}\)
= \(\frac{5}{6}+\frac{5}{6}\)
= \(\frac{10}{6}\)
= \(\frac{5}{3}\)
2, Tính rồi rút gọn
a) \(\frac{8}{15}+\frac{2}{3}\)
= \(\frac{8}{15}+\frac{10}{15}\)
= \(\frac{18}{15}\)
= \(\frac{6}{5}\)
b) \(\frac{3}{7}+\frac{4}{8}\)
= \(\frac{24}{56}+\frac{28}{56}\)
= \(\frac{52}{56}\)
= \(\frac{13}{14}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(3-1\right)A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ 2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ 2A=\left(3^4-1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ 2A=\left(3^8-1\right)\left(3^8+1\right)...\left(3^{64}-1\right)\\ ...\\ 2A=\left(3^{64}-1\right)\left(3^{64}+1\right)\\ 2A=3^{128}-1\)
Vậy \(A=\dfrac{3^{128}-1}{2}.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
4 - ( y +15)+32
4 - y - 15 +32
4 - y - 47
4 - 47 - y
(-43 ) - y
![](https://rs.olm.vn/images/avt/0.png?1311)
1) \(B=1+3+3^2+...+3^{1999}+3^{2000}\)
\(3B=3\cdot\left(1+3+3^2+...+3^{2000}\right)\)
\(3B=3+3^2+...+3^{2001}\)
\(3B-B=3+3^2+3^3+...+3^{2001}-1-3-3^2-...-3^{2000}\)
\(2B=3^{2001}-1\)
\(B=\dfrac{3^{2001}-1}{2}\)
2) \(C=1+4+4^2+...+4^{100}\)
\(4C=4\cdot\left(1+4+4^2+...+4^{100}\right)\)
\(4C=4+4^2+4^3+...+4^{101}\)
\(4C-C=4+4^2+4^3+...+4^{201}-1-4-4^2-....-4^{100}\)
\(3C=4^{101}-1\)
\(C=\dfrac{4^{101}-1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
triển khai hđt:
\(\left(a+b\right)^3-3ab\left(a+b\right)=a^3+3a^2b+3ab^2+b^3-3a^2b-3ab^2\)
\(=a^3+b^3\)