Question

Tính tổng :\(P=\frac{1}{2\cdot3}+\frac{1}{6\cdot5}+\frac{1}{10\cdot7}+...+\frac{1}{198\cdot101}\)

Answer 1

Bai nay mk vua giai xong nen ko muon giai nua

mk chi neu cach giai thoi

dau tien tinh 1/2P ra quy luat o mau la 2.6 ; 6.10 ; 10.14 ; ...; 198.202 roi nhan voi 4 la ra

Ket qua la 25/101

Answer 2

kết quả là \(\frac{25}{101}\)

Answer 3

\(P=\frac{1}{2.3}+\frac{1}{6.5}+............+\frac{1}{198.101}\)

\(P=\frac{1}{6}+\frac{1}{30}+.........+\frac{1}{19998}\)

\(\frac{1}{2}P=\frac{1}{12}+\frac{1}{60}+...........+\frac{1}{39996}\)

\(\frac{1}{2}P=\frac{1}{2.6}+\frac{1}{6.10}+.........+\frac{1}{198.202}\)

\(\frac{1}{2}P=\frac{1}{4}.\left(\frac{4}{2.6}+\frac{4}{6.10}+..........+\frac{4}{198.202}\right)\)

\(\frac{1}{2}P=\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+..........+\frac{1}{198}-\frac{1}{202}\right)\)

\(\frac{1}{2}P=\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{202}\right)\)

\(\frac{1}{2}P=\frac{1}{4}.\frac{50}{101}\)

\(\frac{1}{2}P=\frac{25}{202}\)

\(P=\frac{25}{202}:\frac{1}{2}\)

\(P=\frac{25}{101}\)