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s= (2/1.2.3 +2/2.3.4+...+2/98.99.100):2= (1/1.2-1/2.3+1/2.3-1/3.4+...+1/98.99-1/99.100):2=(1/1.2-1/99.100):2=4949/19800=>S=4949/19800
\(E=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)
\(E=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)
\(E=\frac{1}{1.2}-\frac{1}{99.100}\)
rồi đấy tự tính tiếp
Đặt A=1.2.3+2.3.4+...+98.99.100
4A=1.2.3.4+2.3.4.4+...+98.99.100.4
4A=1.2.3.(4-0)+2.3.4.(5-1)+...+98.99.100.(101-97)
4A=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+98.99.100.101-97.98.99.100
4A=(1.2.3.4+2.3.4.5+...+98.99.100.101)-(0.1.2.3+1.2.3.4+...+97.98.99.100)
4A=98.99.100.101-0.1.2.3
4A=98.99.100.101
A=98.99.25.101
A=24497550
Đặt S=1.2.3+2.3.4+...+98.99.100
4S=1.2.3.(4 - 0)+2.3.4.(5 - 1)+...+98.99.100.(101 - 97)
4S=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+98.99.100.101-97.98.99.100
4S=(1.2.3.4+2.3.4.5+...+98.99.100.101) - (0.1.2.3+1.2.3.4+...+97.98.99.100)
4S=98.99.100.101-0.1.2.3
4S=98.99.100.101
S=98.99.25.101
S=24497550
mình làm cách cấp 2
A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ........ + 98.99.(100 - 97)
A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ........ + 98.99.100 - 97.98.99
A = (1.2.3 + 2.3.4 + 3.4.5 + ....... + 98.99.100) - (1.2.3 + 2.3.4 + ..... + 97.98.99)
A = 98.99.100
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4
4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100
4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101
4A=98.99.100.101
=>A=98.99.100.101/4