Xét vế phải\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{199}-\frac{1}{200}\)

=\(\left(1+\frac{1}{3}+\frac{1}{5}+..+\frac{1}{199}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200}\right)\)

=\(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{199}+\frac{1}{200}\right)-2.\left(\frac{1}{2}-\frac{1}{4}-...-\frac{1}{200}\right)\)

=\(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{199}+\frac{1}{200}-1-\frac{1}{2}-...-\frac{1}{100}\)

=\(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)

Làm ơn giải giúp mình nhanh nhanh nhé, mình đang cần gấp, ai giải được mình k cho

chứng minh cái gì bạn

1/101+1/102+..+1/200=(1+1/2+1/3+...+1/100)+1/101+1/102+1/103+...+1/200-(1+1/2+1/3+...+1/100)

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

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

=1-1/2+1/3-1/4+1/5-1/6+...+1/199-1/200

suy ra ĐPCM

nguyen thieu cong thanh ơi cho mình hỏi:

sao lại là :2(1/2+1/4+1/6+...+1/200)

phải là : (1/2+1/4+1/6+...+1/200) chứ

đúng hok?????

Xét vế trái: 1-1/2+1/3-1/4+1/5-1/6+...+1/199-1/200

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

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

=1+1/2+1/3+1/4+1/5+..+1/199+1/200-1-1/2-...-1/100

=1/101+1/102+1/103+...1/200

Vậy vế trái bằng vế phải

Lời giải:

$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}$

$=(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{199})-(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200})$

$=(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+>..+\frac{1}{199}+\frac{1}{200})-2(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200})$

$=(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{199}+\frac{1}{200})-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100})$

$=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}$

i

help me