So sánh A và B :
\(A=\frac{7^{15}}{1+7+7^2+7^3+7^4+...+7^{14}}\)
\(B=\frac{9^{15}}{1+9+9^2+9^3+9^4+...+9^{14}}\)
Mk đang cần gấp
Ai nhanh Thì Tick
So sánh:
a)\(\frac{7^{15}}{1+7+7^2+...+7^{14}}\) và \(\frac{9^{15}}{1+9+9^2+...+9^{14}}\)
b) \(\frac{1+3+3^2+...+3^{10}}{1+3+3^2+...+3^9}\)và \(\frac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}\)
a) Đặt \(A=\frac{7^{15}}{1+7+7^2+...+7^{14}}\)
Đặt \(B=1+7+7^2+...+7^{14}\)
\(\Rightarrow7B=7+7^2+...+7^{15}\)
\(\Rightarrow7B-B=6B=7^{15}-1\)
\(\Rightarrow B=\frac{7^{15}-1}{6}\)
\(\Rightarrow A=\frac{7^{15}-1+1}{\frac{7^{15}-1}{6}}=\left(7^{15}-1\right).\frac{6}{7^{15}-1}+\frac{6}{7^{15}-1}=6+\frac{6}{7^{15}-1}\)
Tự làm tiếp nha
A=\(\frac{7^{15}}{1+7+7^2+...+7^{14}}\) B=\(\frac{9^{15}}{1+9+9^2+...+9^{14}}\)
So sánh A và B
Help me!!!!!
So sánh:
a)\(\frac{7^{15}}{1+7+7^2+...+7^{14}}\) và \(\frac{9^{15}}{1+9+9^2+...+9^{14}}\)
b) \(\frac{1+3+3^2+...+3^{10}}{1+3+3^2+...+3^9}\)và \(\frac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}\)
b, Ta có:\(\dfrac{1+3+3^2+.....+3^{10}}{1+3+3^2+.....+3^9}\) \(=\dfrac{1}{1+3+3^2+...+3^9}+\dfrac{3+3^2+...+3^{10}}{1+3+3^2+...+3^9}\)\(=\dfrac{1}{1+3+3^2+...+3^9}+\dfrac{3.\left(1+3+3^2+...+3^9\right)}{1+3+3^2+...+3^9}\)
\(=\dfrac{1}{1+3+3^2+...+3^9}+3< 4\)
\(\Rightarrow\) \(\dfrac{1+3+3^2+...+3^{10}}{1+3+3^2+...+3^9}< 4\) \(\left(1\right)\)
Ta có :\(\dfrac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}\)
\(=\dfrac{1}{1+5+5^2+...+5^9}+\dfrac{5+5^2+...+5^{10}}{1+5+5^2+....+5^9}\)
\(=\dfrac{1}{1+5+5^2+...+5^9}+\dfrac{5.\left(1+5+5^2+...+5^9\right)}{1+5+5^2+...+5^9}\)
\(=\dfrac{1}{1+5+5^2+...+5^9}+5>5\)
\(\Rightarrow\) \(\dfrac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}>5\) \(\left(2\right)\)
Từ \(\left(1\right)và\left(2\right)\)
\(\Rightarrow\dfrac{1+3+3^2+...+3^{10}}{1+3+3^2+...+3^9}< \dfrac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}\)
Vậy \(\dfrac{1+3+3^2+...+3^{10}}{1+3+3^2+...+3^9}< \dfrac{1+5+5^2+...+5^{10}}{1+5+5^2+...+5^9}\)
a, Đặt \(A\)\(=\dfrac{7^{15}}{1+7+7^2+...+7^{14}}\)
\(\Rightarrow\) \(\dfrac{1}{A}\) \(=\dfrac{1+7+7^2+...+7^{14}}{7^{15}}=\dfrac{1}{7^{15}}+\dfrac{7}{7^{15}}+\dfrac{7^2}{7^{15}}+...+\dfrac{7^{14}}{7^{15}}\)
\(=\dfrac{1}{7^{15}}+\dfrac{1}{7^{14}}+\dfrac{1}{7^{13}}+....+\dfrac{1}{7}\)
Đặt \(B=\dfrac{9^{15}}{1+9+9^2+...+9^{14}}\)
\(\Rightarrow\dfrac{1}{B}=\dfrac{1+9+9^2+...+9^{14}}{9^{15}}=\dfrac{1}{9^{15}}+\dfrac{9}{9^{15}}+\dfrac{9^2}{9^{15}}+...+\dfrac{9^{14}}{9^{15}}\)
\(=\dfrac{1}{9^{15}}+\dfrac{1}{9^{14}}+\dfrac{1}{9^{13}}+...+\dfrac{1}{9}\)
Mà \(\dfrac{1}{7^{15}}>\dfrac{1}{9^{15}};\dfrac{1}{7^{14}}>\dfrac{1}{9^{14}};\dfrac{1}{7^{13}}>\dfrac{1}{9^{13}};....;\dfrac{1}{7}>\dfrac{1}{9}\)
\(\Rightarrow\dfrac{1}{A}>\dfrac{1}{B}\) \(\Rightarrow A< B\)
Vậy\(\dfrac{7^{15}}{1+7+7^2+...+7^{14}}>\dfrac{9^{15}}{1+9+9^2+....+9^{14}}\)
Mình sửa kết luận
Vậy\(\dfrac{7^{15}}{1+7+7^2+...+7^{14}}< \dfrac{9^{15}}{1+9+9^2+...+9^{14}}\)
tính giá trị biểu thức
[a] 1/3-2/15+14/15
[b] 3/5 +4-6/7
[c] 1/7+2/9+3/10+7/9+6/7+7/10
[d]3/4+5/8-5/6
mình cần gấp,các bạn trả lời nhanh giúp mình với ạ
\(\dfrac{1}{3}\)-\(\dfrac{2}{15}\)+\(\dfrac{14}{15}\)=\(\dfrac{3}{15}\)-\(\dfrac{2}{15}\)+\(\dfrac{14}{15}\)
=\(\dfrac{13}{15}\)
\(\dfrac{3}{5}\)+4-\(\dfrac{6}{7}\)=\(\dfrac{3}{5}\)+\(\dfrac{20}{5}\)-\(\dfrac{6}{7}\)=\(\dfrac{23}{5}\)-\(\dfrac{6}{7}\)=\(\dfrac{161}{35}\)-\(\dfrac{30}{35}\)=\(\dfrac{131}{35}\)
a,-8/3+7/5+-71/15<x<-13/7+19/14+-7/2
b,-19/6+-15/2+11/3<x<-5/4+19/12+-10/3
c,-6/7+3/35<x<-2/5+3/7
d,x=3/4+1/-12
e,x/14=1/7+-3/14
f,11/18+13/6=85/x
g,8/17+5/17<x/17<6/17+9/17
mong các bn giúp đỡ mk vs mk cần rát gấp
ai nhanh giúp mk thì mk tick cho 3 tick mk thề có lòng tự trọng
ai lm nhanh mk cho 10 tick lun nhanh nha đang cần gấp
các bn lm đến đâu cx dc miễn là lm hộ mk cái ạ, ai đang lm vào nhắn tin vs mk để mk bít nha
a; \(-\dfrac{8}{3}+\dfrac{7}{5}-\dfrac{71}{15}< x< -\dfrac{13}{7}+\dfrac{19}{14}-\dfrac{7}{2}\)
-\(\dfrac{19}{15}\) - \(\dfrac{71}{15}\) < \(x\) < -\(\dfrac{1}{2}\) - \(\dfrac{7}{2}\)
-6 < \(x\) < -4
vì \(x\) \(\in\) Z nên \(x\) = -5
- \(\dfrac{19}{6}+\dfrac{-15}{2}+\dfrac{11}{3}\) < \(x\) < - \(\dfrac{5}{4}\) + \(\dfrac{19}{12}\) - \(\dfrac{10}{3}\)
- \(\dfrac{32}{3}+\dfrac{11}{3}< x< \) \(\dfrac{1}{3}\) - \(\dfrac{10}{3}\)
-7 < \(x\) < - 3
Vì \(x\in\) Z nên \(x\in\) {-6;-5;-4}
Tính nhanh:
M=\(\frac{-7}{9}.\frac{15}{49}.\frac{9}{7}.15.\frac{14}{15}\)
N=\(\frac{5}{9}.\frac{4}{7}.\frac{10}{3}+\frac{15}{45}.\frac{3}{7}.\frac{1}{2}\)
\(M=\frac{\left(-7\right).15.9.15.14}{9.49.7.15}=\frac{-15.2}{7}=\frac{-30}{7}.\)
\(N=\frac{200}{189}+\frac{1}{14}=\)1.12962962963
\(M=\left(\frac{-7}{9}\cdot\frac{9}{7}\right)\cdot\left(\frac{15}{49}\cdot\frac{14}{15}\right)\cdot15\)
\(M=\left(-1\right)\cdot\frac{2}{7}\cdot15\)
\(M=\frac{-30}{7}\)
\(N=\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{10}{3}+\frac{3}{9}\cdot\frac{3}{7}\cdot\frac{1}{2}\)
\(N=\frac{200\cdot2}{189\cdot2}+\frac{9\cdot3}{126\cdot3}\)
\(N=\frac{400}{378}+\frac{27}{378}\)
\(N=\frac{61}{51}\)
T i ck nha
Giải giùm mk zới mn~~~~tặng người đầu tiên làm 4 tick nha(đảm bảo lên 4 điểm 100%)
a)\(\frac{-4}{9}.\frac{7}{15}+\frac{4}{-9}.\frac{8}{15}\)
b)\(\frac{5}{-4}.\frac{16}{25}+\frac{-5}{4}.\frac{9}{25}.\)
c)\(4\frac{11}{23}-\frac{9}{14}+2\frac{12}{23}-\frac{5}{4}.\)
d)\(2\frac{13}{27}-\frac{7}{15}+3\frac{14}{27}-\frac{8}{15}\)
e)\(11\frac{1}{4}-\left\{2\frac{5}{7}+5\frac{1}{4}\right\}\)
g)\(\frac{7}{19}.\frac{8}{11}+\frac{7}{19}.\frac{3}{11}+\frac{12}{19}\)
â, -4/9(7/15+8/15)=-4/9
b,-5/4(16/25+9/25)=-5/4
,.....
dài quá mik làm ko hết
hok tốt
1. Tính
a, 11/15 + - 7/10 + 13/30
b, 7/9 + -1/4 + 3/5
c, -5/21 + -5/14 + 4/35
d, 2/7 + 1/9 + 1/7 + 5/9 + 8/14
e, -4/9 + 8/15 + -2/11 + 5/-9 + 7/15
1) so sánh phân số
a) -8/12 và -3/-4 b)-56 /24 và 7/3 c) -4/25 và 15/-13
2) tính
a) 3/5 x 20/ -9
b)4/15 + -3/2 +8/-5
c) 19/35 x -38/7
d) -7/12 x 13/14 +1/14 x (-7) /12
Bài 1:
a: -8/12<0<-3/-4
b: -56/24<0<7/3
c: 4/25<1<15/13
=>-4/25>-15/13
Bài 2:
a: =-60/45=-4/3
b: =4/15-3/2-8/5=8/30-45/30-48/30=-85/30=-17/6