( \(\frac{2048}{2049}\) + 12345 + 875 - 7 ) *\(\frac{1}{2016}\) * 0 = ???
Cho 2048 số nguyên dương a1,a2,a3,................,a2048 thỏa mãn:
\(\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+............+\frac{1}{a_{2048}}=200\)
Chứng minh rằng tồn tại ít nhất hai trong 2048 số bằng nhau
\(\left(\frac{1}{2}+\frac{2015}{2016}+\frac{2016}{2017}+1\right)\left(\frac{2105}{2016}+\frac{2016}{2017}+\frac{7}{22}\right)-\left(\frac{1}{2}+\frac{2015}{2016}+\frac{2016}{2017}\right)\left(\frac{2015}{2016}+\frac{2016}{2017}+\frac{7}{22}+1\right)\)
Tính S = \(\left(\frac{-1}{7}\right)^0+\left(-\frac{1}{7}\right)^1+\left(-\frac{1}{7}\right)^2+.....+\left(-\frac{1}{7}\right)^{2016}\)
S= -(1/7^0 + 1/7^1+ 1/7^2 + 1/7^3 +...+ 1/7^2016)
Xét A = 1/7^0 + 1/7^1 + 1/7^2 + 1/7^3 +...+ 1/7^2016
=>7A= 7 + 1/7^0 + 1/7^1 + ...+ 1/7^2015
=> 6A = 7 - 1/7^2016
=> A = (7 - 1/7^2016)/6
=>S=-(7-1/7^2016)/6
Tính giá trị biểu thức :
\(A=\frac{1}{2016^{-2016}+1}+\frac{1}{2016^{-2015}+1}+..............+\frac{1}{2016^{-1}+1}+\frac{1}{2016^0+1}+\frac{1}{2016^1+1}+.............+\frac{1}{2016^{2016}+1}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2048}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2048}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-...-\frac{1}{2048}+\frac{1}{2048}\)
\(=1-\frac{1}{2048}\)
\(=\frac{2047}{2048}\)
k mk nha
Đặt A = 1/21 + 1/22 + 1/23 + 1/24 +... +1/211
2A = (1/21 + 1/22 + 1/23 + 1/24 +... +1/211).2
2A = 1 + 1/2 +1/22 + ...+ 1/210
2A - A = ( 1 + 1/2 +1/22 + ...+ 1/210 ) - (1/21 + 1/22 + 1/23 + 1/24 +... +1/211)
A = 1 - 1/211
A = 1 - 1/2048
A = 2047/2048
NHA CÁC BẠN ^_^
Đặt S = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2048
2.S = 1 + 1/2 + 1/4 + 1/8 + ... + 1/2048
2.S - S = ( 1 + 1/2 + 1/4 + 1/8 + ... + 1/2048 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2048 )
S = 1 - 1/2048
S = 2047/2048
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{2048}\)
tất cả rút gọn = 1 /2
và GẠCH TỬ SỐ,MẪU SỐ GIỐNG NHAU
kết quả = 1 nhé
Coi mk làm nha
1/2+1/4+1/8+....+1/2048
=1+1/2+1/4+1/8+.....+1/2048
=(1+1/2+.....+1/2048)-(1/2+1/4+...+1/2048)
=1-1/2048
=2047/2048
Tính P=\(\frac{0,,75-0,6+\frac{3}{7}+\frac{3}{13}}{2,75-2,2+\frac{11}{7}+\frac{11}{13}}\)
Tính B=\(\frac{1}{3}+\frac{1}{^{3^2}}+\frac{1}{3^3}+................+\frac{1}{3^{2015}}+\frac{1}{3^{2016}}\)
\(P=\frac{0,75-0,6+\frac{3}{7}+\frac{3}{13}}{2,75-2,2+\frac{11}{7}+\frac{11}{13}}\)
\(P=\frac{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}+\frac{3}{13}}{\frac{11}{4}-\frac{11}{5}+\frac{11}{7}+\frac{11}{13}}\)
\(P=\frac{3\cdot\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}{11\cdot\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}=\frac{3}{11}\)
\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{2015}}+\frac{1}{3^{2016}}\)
\(\frac{1}{B}=3+3^2+3^3+...+3^{2015}+3^{2016}\)
\(\frac{3}{B}=3^2+3^3+3^4+...+3^{2016}+3^{2017}\)
\(\frac{3}{B}-\frac{1}{B}=\left(3^2+3^3+3^4+...+3^{2016}+3^{2017}\right)-\left(3+3^2+3^3+...+3^{2015}+3^{2016}\right)\)
\(\frac{2}{B}=3^{2017}-3\)
\(B=\frac{2}{3^{2017}-3}\)
P=\(\frac{0,75-0,6+\frac{3}{7}+\frac{3}{13}}{2,75-2,2+\frac{11}{7}+\frac{11}{13}}\)
P=\(\frac{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}+\frac{3}{13}}{\frac{11}{4}-\frac{11}{3}+\frac{11}{7}+\frac{11}{3}}\)
P=\(\frac{\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}{\frac{1}{11}.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}\)
P=\(\frac{\frac{1}{3}}{\frac{1}{11}}=\frac{1}{3}:\frac{1}{11}=\frac{11}{3}\)
B=\(\frac{1}{3}+\frac{1}{^{3^2}}+\frac{1}{3^3}+................+\frac{1}{3^{2015}}+\frac{1}{3^{2016}}\)
B=\(\left(\frac{1}{3}\right)^1+\left(\frac{1}{3}\right)^2+\left(\frac{1}{3}\right)^3+...+\left(\frac{1}{3}\right)^{2015}+\left(\frac{1}{3}\right)^{2016}\)
2B=\(\left(\frac{1}{3}\right)^2+\left(\frac{1}{3}\right)^3+\left(\frac{1}{3}\right)^4+...+\left(\frac{1}{3}\right)^{2016}+\left(\frac{1}{3}\right)^{2017}\)
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B=\(\left(\frac{1}{3}\right)^1+\left(\frac{1}{3}\right)^2+\left(\frac{1}{3}\right)^3+...+\left(\frac{1}{3}\right)^{2015}+\left(\frac{1}{3}\right)^{2016}\)
B=\(\left(\frac{1}{3}\right)^1-\left(\frac{1}{3}\right)^{2017}\)
cho a,b,c>0 thõa mãn abc=1. CM \(\frac{1}{a^{2016}+b^{2016}+1}+\frac{1}{b^{2016}+c^{2016}+1}+\frac{1}{c^{2016}+a^{2016}+1}\le1\)
e ơi e nên tải tài liệu của võ quốc bá cẩn đi
Cho dãy số có quy luật :
\(0,\frac{1}{6},\frac{7}{20},\frac{27}{50},\frac{11}{15},\frac{13}{14},\frac{9}{8},....\)
Tìm số thứ 2016 .
quá dễ ko chị đâu ko biết thì nghỉ học đi