Question

Giúp mình với

1/2+1/3+1/4+...+1/100

Answer 1

99/100

Answer 2

Đặt :

\(S=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+.......+\dfrac{1}{100}\)

\(\Rightarrow2S=2+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+.......+\dfrac{1}{100}\)

\(\Rightarrow2S-S=\left(2+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+.........+\dfrac{1}{100}\right)\)

\(\Rightarrow S=2-\dfrac{1}{100}=\dfrac{199}{100}\)

 

Answer 3

Answer 4

 

Đặt :

S=1/2+1/3+1/4+.......+1/100

⇒2S=2+1/2+1/3+1/4+.......+1/100

⇒2S−S=(2+1/2+1/3+1/4+.........+1/100)

⇒2S−S=(2+1/2+1/3+1/4+.........+1/100)

⇒S=2−1/100=199/100