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\(S=2.10+2.12+2.14+...+2.20\\ S=2.\left(10+12+14+...+20\right)\\ S=2.\left\{\left[\left(20-10\right):2+1\right].\left(20+10\right):2\right\}\\ S=2.\left\{\left[10:2+1\right].30:2\right\}\\ S=2.\left\{\left[5+1\right].30:2\right\}\\ S=2.\left\{6.30:2\right\}\\ S=2.\left\{180:2\right\}\\ S=2.90\\ S=180\)
TK :
S=2.10+2.12+2.14+...+2.20
S=2.[(10+20)+(12+18)+(14+16)]
S=2.(30+30+30)
S=2.90
S=180
Ta có: \(B=\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}=\frac{5^2.\left(2.3\right)^{11}.\left(4^2\right)^2+\left(2.3\right)^2.\left(2^2.3\right)^6.\left(3.5\right)^2}{2.\left(2.3\right)^{12}.\left(2.5\right)^4-\left(3^4\right)^2.\left(2^6.3.5\right)^3}\)
\(\frac{5^2.2^{11}.3^{11}.2^8+2^2.3^2.2^{12}.3^6.3^2.5^2}{2.2^{12}.3^{12}.2^4.5^4-3^8.2^{18}.3^3.5^3}=\frac{5^2.2^{19}.3^{11}+2^{14}.3^{10}.5^2}{2^{17}.3^{12}.5^4-3^{11}.2^{18}.5^3}\)
\(=\frac{5^2.2^{14}.3^{10}.\left(2^5.3+1\right)}{2^{17}.3^{11}.5^3.\left(3.5-2\right)}=\frac{2^{14}.3^{10}.5^2.97}{2^{17}.3^{11}.5^3.13}=\frac{1.1.1.97}{2^3.3.5.13}=\frac{97}{1560}\)
\(B=\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)
\(B=\frac{5^2.2^{11}.3^{11}.2^{4^2}+2^2.3^2.2^{2^6}.3^6.3^2.5^2}{2.2^{12}.3^{12}.10^4-3^{4^2}.2^{5^3}.3^3}\)
\(B=\frac{5^2.2^{11}.2^8.3^{11}+2^2.2^{12}.3^2.3^6.3^2.5^2}{2^{13}.3^{12}.10^4-3^8.3^3.2^{15}}\)
\(B=\frac{5^2.2^{19}.3^{11}+2^{14}.3^{10}.5^2}{2^{13}.3^{12}.10^4-3^{11}.2^{15}}\)
\(B=\frac{5^2.2^{14}.3^{10}.\left(2^5.3+1\right)}{2^{13}.3^{11}.\left(3.10^4-2^2\right)}\)
\(B=\frac{5^2.2^{14}.3^{10}.97}{2^{13}.3^{11}.29996}\)
\(B=\frac{5^2.2.97}{3.29996}\)
\(B=\frac{4850}{89988}\)
\(B=\frac{2425}{44994}\)
\(S=2\cdot10+2\cdot12+2\cdot14+...+2\cdot20\)
\(S=2\cdot\left(10+12+14+16+18+20\right)\)
\(S=2\cdot\left[\left(20+10\right)\cdot6:2\right]\)
\(S=2\cdot90=180\)
\(S=2\cdot10+2\cdot12+2\cdot14+\dots+2\cdot20\\=2\cdot(10+12+14+\dots+20)\)
Đặt \(A=10+12+14+\dots+20\)
Số các số hạng của $A$ là:
$(20-10):2+1=6$ (số)
Tổng $A$ bằng:
$(20+10)\cdot6:2=90$
Thay $A=90$ vào $S$, ta được:
$S=2\cdot90=180$
\(S=\frac{8.2+2.14+2.90+2.6+2.12}{2.3.4+2.8+2.79+2.11}\)
\(=\frac{2\left(8+14+90+6+12\right)}{2\left(3.4+8+79+11\right)}\)
\(=\frac{130}{110}\)
\(=\frac{13}{11}\)
\(S=\frac{2\cdot\left(8+14+90+6+12\right)}{2.\left(3.4+8+79+11\right)}=\frac{2.130}{2.110}=\frac{130}{110}=\frac{13}{11}\)
Nếu đúng cho L ike nhé !