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P=1/1.2.3.4 +1/2.3.4.5 +1/3.4.5.6 +...+1/97.98.99.100
3P=3/1.2.3.4 +3/2.3.4.5 +3/3.4.5.6 +...+3/97.98.99.100
3P=1/1.2.3-1/2.3.4+1/2.3.4-1/3.4.5+................+1/97.98.99-1/98.99.100
3P = 1/1.2.3 - 1/98.99.100
3P =( 98.99.100-1.2.3)/1.2.3.98.99.100
P=( 98.99.100-1.2.3)/1.2.3.98.99.100.3
P=(98.33.50-1)/98.99.100.3
P= 161699/2910600
=1/1.2-1/3.4+1/2.3-1/3.4+...+1/116.117-1/118.119
=1-1/2-1/3+1/4+1/2-1/3-1/3-1/4+...+1/116-1/117-1/118+1/119
=1+1/119=120/119(ko nhầm thì z)
P = 1/1.2.3.4 + 1/2.3.4.5 + 1/3.4.5.6 + ... + 1/97.98.99.100
P = 1/1-1/2-1/3-1/4+1/2-1/3-1/4-1/5 +....+1/97-1/98-1/99-1/100
P = 1/1-1/100
P = 99/100
Tính giá trị biểu thức P.3.98.99
Cái đó thì bạn tự tính cũng dc dễ mak
F= \(\frac{1}{1.2.3}\)- \(\frac{1}{2.3.4}\)+ \(\frac{1}{2.3.4}\)- \(\frac{1}{3.4.5}\)+....+\(\frac{1}{47.48.49}\)- \(\frac{1}{48.49.50}\)
F=\(\frac{1}{1.2.3}\)- \(\frac{1}{48.49.50}\)
F=\(\frac{6533}{39200}\)
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100} \)
\(=\frac{1}{3}.\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)=\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)=\frac{1}{18}-\frac{1}{6.970200}\)
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100}\)
=\(\frac{1}{3}\cdot\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{4.5.6}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)\)
=\(\frac{1}{18}-\frac{1}{5821200}\)
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100}=\frac{1}{3}.\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)=\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)=\frac{1}{18}-\frac{1}{6.970200}\)
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100}\)
\(=\frac{1}{3}.\left(\frac{3}{1.2.3.4}+ \frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)\)
\(=\frac{1}{3}.\frac{161699}{970200}=\frac{161699}{299106000}\)