(-1).(-13)
1+13^4+13^8+...+13^96+13^100/1+13^2+13^4+...+13^98+13^100+13^102
so sánh : C=13^15+1/13^14+1 và D=13^14+1/13^13+1
B= 1+1/13+1/13²+1/13³+...+1/13 mũ n( n thuộc N*)
\(B=1+\dfrac{1}{13}+\dfrac{1}{13^2}+...+\dfrac{1}{13^n}\)
\(=>13B=13+1+\dfrac{1}{13}+...+\dfrac{1}{13^{n-1}}\)
\(=>13B-B=13-\dfrac{1}{13^n}\)
\(=>12B=\dfrac{13^{n+1}-1}{13^n}\)
\(=>B=\dfrac{13^{n+1}-1}{13^n.12}\)
\(#Nttnam\)
\(\dfrac{\sqrt{13}}{\sqrt{\sqrt{13}+1-1}}-\dfrac{\sqrt{13}}{\sqrt{\sqrt{13}+1+1}}\)
\(\dfrac{\sqrt{13}}{\sqrt{\sqrt{13}+1-1}}-\dfrac{\sqrt{13}}{\sqrt{\sqrt{13}+1+1}}\\ =\dfrac{\sqrt{13}}{\sqrt{\sqrt{13}}}-\dfrac{\sqrt{13}}{\sqrt{\sqrt{13}+2}}\\ =\sqrt{\dfrac{13}{\sqrt{13}}}-\sqrt{\dfrac{13}{\sqrt{13}+2}}\\ =\sqrt[4]{13}-\sqrt{\dfrac{13\sqrt{13}-26}{9}}\\=\sqrt[4]{13}-\dfrac{\sqrt{13\sqrt{13}-26} }{3}\\ =\dfrac{3\sqrt[4]{13}-\sqrt{13\sqrt{13}-26}}{3}\)
so sanh A= 13^15 + 1/13^6 +1 va B= 13^16 + 1/13^ 7+1
\(A=\frac{1+13^4+13^8+..+13^{96}+13^{100}}{1+13^2+13^4+..+13^{98}+13^{102}}\)TÍNH A
A=\(\dfrac{13^{15}+1}{13^{16}+1}\) và B= \(\dfrac{13^{16}+1}{13^{17}+1}\)
so sánh A và B
\(ta có A=\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{15}}{13^{16}}+1\)=\(\dfrac{1}{13}+1\)
B=\(\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{16}}{13^{17}}+1\)=\(\dfrac{1}{13}+1\)
vậy A=B
\(A=\dfrac{13^{15}+1}{13^{16}+1}vàB=\dfrac{13^{16}+1}{13^{17}+1}\)
ta có
\(\dfrac{13^{16}+1}{13^{17}+1}< 1\Rightarrow\dfrac{13^{16}+1+12}{13^{17}+1+12}=\dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\dfrac{13^{15}+1}{13^{16}+1}=A\)
vậy B<A
\(A=\dfrac{13^{15}+1}{13^{16}+1}vàB=\dfrac{13^{16}+1}{13^{17}+1}\)
ta có B<1 nên
\(\dfrac{13^{16}+1}{13^{17}+1}< \dfrac{13^{16}+1+12}{13^{17}+1+12}=\dfrac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\dfrac{13^{15}+1}{13^{16}+1}=A\)
Vậy B<A
So sánh 10^2000+5/10^2001-8 và 10^2000+6/10^2001-7
Tính 1+13^4+13^8+...+13^96+13^100/1+13^2+13^4+...+13^98+13^100+13^102
Tính A=2/5.7+5/7.12+9/19.28+11/28.39+1/39.40
Tính giúp mình với !!!!!
1/13 . 8/13- 14/13 + 5/13 . 1/13
1/13.(8/13-5/13)+14/13
1/13.3/13+14/13
3/13+14/13
17/13
NHƯ VẦY ĐÓ BẠN MIK CŨNG HỌC LỚP 6 NHƯ BẠN ĐÓ
1/13 . 8/13 + 5/13 . 1/13 - 14/13
= 1/13 . (8/13 + 5/13) - 14/13
= 1/13 . 13/13 - 14/13
= 1/13 . 1 - 14/13
= 1/13 - 14/13
= -13/13
= -1