Đặt :
\(S=\frac{1}{1.3}+...+\frac{1}{99.101}\)
\(S=\frac{1}{1}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{99}-\frac{1}{101}\right)\)
\(S=\frac{1}{1}.\left(\frac{1}{1}-\frac{1}{101}\right)\)
\(S=\frac{1}{1}.\frac{100}{101}\)
\(S=\frac{100}{101}\)
=1/2(2/1.3+2/3.5+2/5.7+............+2/99.101)
=1/2(1-1/3+1/3-1/5+...........+1/99-1/101)
=1/2(1-1/101)
=1/2.100/101=50/101
HAY LA 100/101 Y
HIHI
1/1.3 + 1/ 3.5 + .............+ 1/99.101
= 1 - 1/3 + 1/3 - 1/5 + .........+ 1/99 - 1/101
= 1 - 1/101
= 100/101
đặt S = 1/1.3 + 1/3.5 + ... + 1/99.101
S = 1/1 - 1/3 + 1/3 - 1/5 + ... + 1/99 - 1/101
S = 1/1 + (-1/3 + 1/3) + (-1/5 + 1/5)+ ... + (-1/99 + 1/99) - 1/101
S = 1/1 + 0 + 0 + ... + 0 - 1/101
S = 1/1 - 1/101
S = 101/101 - 1/101
S = 100/101
mong bạn thông cảm ! đúng thì k cho mình nhé !
\(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{99.101}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\frac{100}{101}\)
\(=\frac{50}{101}\)