Áp dụng công thức \(1+2+...+n=\frac{n\left(n+1\right)}{2}\)ta có:

\(E=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{200}\left(1+2+...+200\right)\)

\(=1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+....+\frac{1}{200}.\frac{200.201}{2}\)

\(=1+\frac{3}{2}+\frac{4}{2}+....+\frac{201}{2}\)

\(=\frac{2+3+4+...+201}{2}=\frac{\frac{201.202}{2}-1}{2}=10150\)

10150

`2/5+1/4`

`=8/20+5/20`

`=13/20`

__

`1/3+3/5`

`=5/15+9/15`

`=14/15`

__

`1/2+1/4`

`=2/4+1/4`

`=3/4`

__

`1/8+5/6`

`=6/48+40/48`

`=46/48`

`=23/24`

2/5 + 1/4
= 8/20 + 5/20
= 13/20
1/3 + 3/5
= 5/15 + 9/15
= 14/15
1/2 + 1/4
= 2/4 + 1/4
= 3/4
1/8 + 5/6
= 6/48 + 40/48
= 46/48
= 23/24

S=(1-2)+(3-4)+(5-6)+...+(199-200)

S=(-1)+(-1)+...+(-1)

S=(-1).100=-100

S=1+(2-3)+(-4+5)+...+(98-99)+(-100+101)

S=1+(-1)+1+..+(-1)+1

S=1+25.(-1)+25.1

S=1+(-25)+25

S=1+0

=1

Nhanh nha mk cần gấp đó!

S= 1+(1-3)+3+(1-5)+5+(1-7)+........+199+(1-199)=200

Số số hạng:(200-1)+1=200

Tổng:200(200+1):2=20100

tick mk nha

a) \(D=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)

\(\Rightarrow7D=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{99}}\)

\(\Rightarrow7D-D=\left(1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{99}}\right)-\left(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\right)\)

\(\Rightarrow6D=1-\frac{1}{7^{100}}\)

\(\Rightarrow D=\left(1-\frac{1}{7^{100}}\right).\frac{1}{6}\)

\(15.95+5.95-\left(3^2\right)^3+5^7:5^4\)

\(=\left(15+5\right).95-3^6+5^2\)

\(=20.95-729-25\)

\(=1900-729-25\)

\(=1171-25\)

\(=1146\)

\(15.95+5.95-\left(3^2\right)^3+5^7:5^4\)

\(=\left(15+5\right)\cdot95-3^6+5^3\)

\(=20\cdot95-729-125\)

\(=1900-729-125\)

\(=1046\)