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S=2.3+3.4+4.5+....+34.35
3S=2.3.3+3.4.3+4.5.3+...+34.35.3
3S=2.3.(4−1)+3.4.(5−2)+4.5.(6−3)+...+34.35.(36−33)
3S=2.3.4−1.2.3+3.4.5−2.3.4+4.5.6−3.4.5+....+34.35.36−33.34.35
3S=34.35.36−6
S=\(\frac{\text{34.35.36−6}}{3}\)
\(3S=3x2x3+3x3x4+..+3x34x35\)
\(3S=3x2\left(4-1\right)\)\(+3x3\left(5-1\right)\)\(+...+34x35\left(36-33\right)\)
\(3S=3x2x4-1x2x3+3x4x5-2x3x4+...+34x35x36-33x34x35\)
\(3S=34x35x36-6\)
\(3S=42834\)
\(S=42834:3=14278\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{200.201}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{200}-\frac{1}{201}\)
\(=1-\frac{1}{201}\)
\(=\frac{200}{201}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{200.201}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{200}-\frac{1}{201}\)
\(=1-\frac{1}{201}=\frac{200}{201}\)
Ủng hộ nha,tớ ko ăn cóp đâu.
Đặt S=1.2+2.3+3.4+...+30.31
Ta có:
3S=1.2.3+2.3.3+3.4.3+...+30.31.3
3S=1.2.3+2.3.(4-1)+3.4.(5-2)+.....+30.31.(32-29)
3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+30.31.32-29.30.31
3S=30.31.32=30.31.32/3=9920
Nhớ
100 số hạng đầu là
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{100.101}\)
ta có \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{100.101}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}=1-\frac{1}{101}\)\(=\frac{100}{101}\)
Bài này mình vừa giải :D http://olm.vn/hoi-dap/question/185493.html -- số khác
Ta có 3 x S = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + ... + 99 x 100 x 3
3 x S = 1 x 2 x (3 - 0) + 2 x 3 x (4 - 1) + 3 x 4 x (5 - 2) + ... + 99 x 100 x (101 - 98)
3 x S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + .. + 99 x 100 x 101 - 98 x 99 x 100
=> 3 x S = 99 x 100 x 101
=> A = 33 x 100 x 101 = 333300
S = 1.2 + 2.3 + 3.4 + 4.5 + ..... + 99.100
3S=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+.....+99.100.(101-98)
3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 99.100.101
3S=99.100.101
S=99.100.101/3
S=333300
\(S=\frac{4}{3\times7}+\frac{4}{7\times11}+\frac{4}{11\times15}+...+\frac{4}{\left(4x-1\right)\times\left(4x+3\right)}\)
\(=\frac{7-3}{3\times7}+\frac{11-4}{7\times11}+\frac{15-11}{11\times15}+...+\frac{\left(4x+3\right)-\left(4x-1\right)}{\left(4x-1\right)\times\left(4x+3\right)}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{4x-1}-\frac{1}{4x+3}\)
\(=\frac{1}{3}-\frac{1}{4x+3}=\frac{664}{1995}\)
\(\Leftrightarrow\frac{1}{4x+3}=\frac{1}{1995}\)
\(\Leftrightarrow4x+3=1995\)
\(\Leftrightarrow x=498\).
Số hạng cuối cùng của dãy \(S\)là: \(\frac{1}{1991\times1995}\).
Tổng \(S\)có \(498\)số hạng.
\(S=2.3+3.4+4.5+...+34.35\)
\(\Rightarrow3S=2.3.\left(4-1\right)+3.4.\left(5-2\right)+4.5.\left(6-3\right)+...+34.35\left(36-33\right)\)
\(=2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+34.35.36-33.34.35\)
\(=34.35.36-1.2.3=42834\)
\(\Rightarrow S=14278\)
41644/3