100 + 965 + ( 1 + 2 ) = ???
Giup minh voi.
1/2x1+1/3x(1+2)+1/4x(1+2+3)+...+1/100x(1+2+3+...+99+100)
Giup minh voi
( 36 : 0,25 - 72 x 2 ) x ( 1 + 2 + 3 +....+100 )
giup minh voi
\(\left(36:0,25-72x2\right)x\left(1+2+3+...+100\right)\)
\(=\left(144-144\right)x\left(1+2+3+...+100\right)\)
\(=0x\left(1+2+3+...+100\right)\)
\(=0\)
1/22 +1/32+....+1/1002<1
giup minh voi
Ta có
\(\frac{1}{2^2}<\frac{1}{1.2}\)
\(\frac{1}{3^2}<\frac{1}{2.3}\)
\(\frac{1}{4^2}<\frac{1}{3.4}\)
......
\(\frac{1}{100^2}<\frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}<1\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}<1\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<1-\frac{1}{100}<1\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}<\frac{99}{100}<1\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{100^2}<1\)
\(\frac{1}{2^2}=\frac{1}{2.2}<\frac{1}{1.2};\frac{1}{3^2}=\frac{1}{3.3}<\frac{1}{2.3};...;\frac{1}{100^2}=\frac{1}{100.100}<\frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+..+\frac{1}{100^2}<\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+..+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+..+\frac{1}{100^2}<1-\frac{1}{100}<1\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}<1\left(đpcm\right)\)
bài này mà lp 8 cái j
Bài này mà lớp 8 ấy !có khi mấy em lớp 6 cũng làm được
Tinh nhanh :
1^2 +2^2 +3^2 +...+100^2
Giup minh voi nhe
Tinh tong S: 1/2x3-2/3x4+....+99/100x101-100/101x102
Cac ban giup minh voi, minh can gap lam!!!
Tim x biet (x+1)(x+2)(x+3)+...+(x+100)=5750
giup minh voi nhe
( x + 1 ) + ( x + 2 ) + ( x + 3 ) +... + ( x + 100 ) = 5750
( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750
( x . 100 ) + ( 1 . 100 ) . 100 : 2 = 5750
( x . 100 ) + 5050 = 5750
x . 100 = 5750 - 5050
x . 100 = 700
x = 700 : 100
x = 7
Vậy x = 7
( x + 1 ) + ( x + 2 ) + ( x + 3 ) +... + ( x + 100 ) = 5750
( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750
( x . 100 ) + ( 1 . 100 ) . 100 : 2 = 5750
( x . 100 ) + 5050 = 5750
x . 100 = 5750 - 5050
x . 100 = 700
x = 700 : 100
x = 7
Vậy x = 7
199 + ( 100 - 50 ) * 2 = ???
Giup minh voi.
199 + ( 100 - 50 ) x 2 = 199 + 50 x 2
= 199 + 100
= 299
199 + ( 100 - 50 ) x 2
= 199 + 50 x 2
= 199 + 100
= 299
\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
giup minh voi
cam on nhieu
cac ban giai chi tiet giup minh nha
\(\frac{1}{\sqrt{a}+\sqrt{a+1}}=\frac{\sqrt{a+1}-\sqrt{a}}{\left(\sqrt{a}+\sqrt{a+1}\right)\left(\sqrt{a+1}-\sqrt{a}\right)}=\frac{\sqrt{a+1}-\sqrt{a}}{a+1-a}=\sqrt{a+1}-\sqrt{a}\Rightarrow\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.......+\frac{1}{\sqrt{99}+\sqrt{100}}=-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-......-\sqrt{99}+\sqrt{100}=10-1=9\)
TINH A=2^100+2^99+2^98+.......+2^1+2^0
CAC BAN GIUP MINH VOI!