Ta có:
\(\dfrac{1}{4^2}< \dfrac{1}{3.4}\)
\(\dfrac{1}{5^2}< \dfrac{1}{4.5}\)
\(\dfrac{1}{6^2}< \dfrac{1}{5.6}\)
\(...\)
\(\dfrac{1}{100^2}< \dfrac{1}{99.100}\)     \(\left(1\right)\)
\(\Rightarrow\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
Đặt \(A=\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=\dfrac{1}{3}-\dfrac{1}{100}\)\(< \dfrac{1}{3}\)     \(\left(2\right)\)
Từ \(\left(1\right)\) và \(\left(2\right)\)
\(\Rightarrow\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{3}\)

k cho minh nha

noichung ai k minh thi minh k cho

Ta có:

A = 1 + ( 2 + 2² + 2³ + 2⁴ ) + ... + 2⁹⁶( 2 + 2² + 2³ + 2⁴ )

A = 1 + 30 + ... + 2⁹⁶ . 30

A = 1 + 30( 1 + 2⁴ + ... + 2⁹⁶ )

Mà 30 chia hết cho 15 nên 30( 1 + 2⁴ + ... + 2⁹⁶ ) chia hết cho 15

\(⇒\) 1 + 30( 1 + 2⁴ + ... + 2⁹⁶ ) : 15 dư 1

\(⇒\) A : 15 dư 1

Thank you

Đặt \(S=\frac{1}{3}+\frac{2}{3^2}+.......+\frac{101}{3^{101}}\)

\(\Rightarrow3S=1+\frac{2}{3}+.......+\frac{101}{3^{100}}\)

\(\Rightarrow3S-S=\left(1+\frac{2}{3}+..+\frac{101}{3^{100}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+..+\frac{101}{3^{101}}\right)\)

\(\Rightarrow2S=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^{100}}-\frac{101}{3^{101}}< 1+\frac{1}{3}+....+\frac{1}{3^{100}}\)

\(\Rightarrow6S< 3+1+........+\frac{1}{3^{99}}\)

\(\Rightarrow6S-2S< \left(3+1+....+\frac{1}{3^{99}}\right)-\left(1+\frac{1}{3}+....+\frac{1}{3^{100}}\right)\)

\(\Rightarrow4S< 3-\frac{1}{3^{100}}< 3\Rightarrow S< \frac{3}{4}\)

Đặt \(A=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}+\frac{101}{3^{101}}\)

\(3A=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}+\frac{101}{3^{100}}\)

\(3A-A=\left(1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{101}{3^{100}}\right)-\left(\frac{1}{3}+\frac{2}{3^2}+...+\frac{101}{3^{101}}\right)\)

\(2A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}-\frac{101}{3^{101}}\)

\(6A=3+1+\frac{1}{3}+...+\frac{1}{3^{99}}-\frac{101}{3^{100}}\)

\(6A-2A=\left(3+1+\frac{1}{3}+...+\frac{1}{3^{99}}-\frac{101}{3^{100}}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}-\frac{101}{3^{101}}\right)\)

\(4A=3-\frac{101}{3^{100}}-\frac{1}{3^{100}}+\frac{101}{3^{101}}\)

\(4A=3-\frac{303}{3^{101}}-\frac{3}{3^{101}}+\frac{100}{3^{101}}\)

\(4A=3-\frac{206}{3^{101}}< 3\)

=>\(4A< 3\)

\(\Rightarrow A< \frac{3}{4}\)

A = 1 + (-2) + (-3) + 4 + 5 + (-6) + (-7) + 8 + .......... + 99 - 100 - 101 + 102 + 103

A = 1 - 2 - 3 + 4 + 5 - 6 - 7 + 8 + ................ + 99 - 100 - 101 + 102 + 103

A = ( 1 - 2 - 3 + 4 ) + ( 5 - 6 - 7 + 8 ) + ............. + ( 99 - 100 - 101 + 102 ) + 103

A = 0 + 0 + ............. + 0 + 103

A = 0 + 103

A = 103

8+2+10+80+100+200+100+500x2+1000-1500

= 1000

Hok tốt

:)

Câu hỏi :

8+2+10+80+100+200+100+500x2+1000-1500=?

Trả lời:

8+2+10+80+100+200+100+500x2+1000-1500 = 1000

Trả lời:

8+2+10+80+100+200+100+500x2+1000-1500=?

= 900

mình ko biết dấu sao lag gì nên lam mò nhé

giả sử sao la dấu nhân

suy ra s<1/1.2+1/2.3+...+1/99.100

s<1/1-1/2+1/2-1/3+...+1/99-1/100

s<1/1-1/100

s<99/100<1

suy ra s<1

nếu sao là dấu cộng

suy ra s=+2/2.3+...+2/100.101

1/2s=1/2-1/3+1/3-1/4+...+1/100-1/101

1/2s=1/2-1/100<1/2

1/2 s <1/2 suy ra s<1
 

thanks ban nhiu nha

\(\Rightarrow A=\left(1+2\right)+\left(2^2+2^3\right)+......+\left(2^{98}+2^{99}\right)\)

\(\Rightarrow A=\left(1+2\right)+2^2\left(1+2\right)+...+2^{98}\left(1+2\right)\)

\(\Rightarrow A=3+2^2.3+....+2^{98}.3\)

\(\Rightarrow A=3\left(1+2^2+....+2^{98}\right)\)

\(Vì3⋮3_{_{ }}\)\(\Rightarrow3\left(1+2^2+...+2^{98}\right)⋮3\)

Vậy Achia hết cho 3

a) A=(1+2-3-4)+(5+6-7-8)+...+(97+98-99-100)

A=(-4)25=-100

=> A chia hết 2;5 không chia hết 3

b, A = 2².5²

A có 9 ước tự nhiên và 18 ước nguyên