cho M=1/101+1/102+1/103+….+1/200 chứng minh rằng M>5/8 giải giúp mik vs nhé mik đang cần gấp

Giải thích các bước giải:

Ta có :
$M=\dfrac{1}{101}+\dfrac{1}{102}+\dfrac{1}{103}+…+\dfrac{1}{200}$

$\to M=(\dfrac{1}{101}+\dfrac{1}{102}+…+\dfrac{1}{125})+(\dfrac{1}{126}+\dfrac{1}{127}+..+\dfrac{1}{150})+(\dfrac{1}{151}+..+\dfrac{1}{175})+(\dfrac{1}{176}+..+\dfrac{1}{200})$

$\to M>(\dfrac{1}{125}+\dfrac{1}{125}+…+\dfrac{1}{125})+(\dfrac{1}{150}+\dfrac{1}{150}+..+\dfrac{1}{150})+(\dfrac{1}{200}+..+\dfrac{1}{200})+(\dfrac{1}{200}+..+\dfrac{1}{200})$

$\to M>\dfrac{25}{125}+\dfrac{25}{150}+\dfrac{25}{175}+\dfrac{25}{200}$

$\to M>\dfrac15+\dfrac16+\dfrac17+\dfrac18$

$\to M>(\dfrac15+\dfrac16+\dfrac17)+\dfrac18$

$\to M>\dfrac{107}{210}+\dfrac18$

$\to M>\dfrac12+\dfrac18=\dfrac58$