Toán Tính `A= 1/1.2 + 1/2.3 + 1/3.4+…+1/19.20` 14/09/2021 By Peyton Tính `A= 1/1.2 + 1/2.3 + 1/3.4+…+1/19.20`
$A=$ $\frac{1}{1.2}$+ $\frac{1}{2.3}$+$\frac{1}{3.4}$+…+$\frac{1}{19.20}$ =1-$\frac{1}{2}$+$\frac{1}{2}$$\frac{1}{3}$+…+$\frac{1}{19}$-$\frac{1}{20}$ = 1-$\frac{1}{20}$ = $\frac{20}{20}$-$\frac{1}{20}$ = $\frac{19}{20}$ Trả lời
$A = \dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + …. + \dfrac{1}{19.20}$ $A = 1 – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{4} + …. + \dfrac{1}{19} – \dfrac{1}{20}$ $A = 1 – \dfrac{1}{20}$ $A = \dfrac{19}{20}$ Công thức chung: $\dfrac{a}{1 + (a+1)} + \dfrac{a}{2 + (a+ 2)} + \dfrac{a}{3 + (a+ 3)} + …. + \dfrac{a}{n +(a+ n)}$ $=\dfrac{1}{1} – \dfrac{1}{a} + \dfrac{1}{2} – \dfrac{1}{a+1} + …. + \dfrac{1}{n} – \dfrac{1}{a+n}$ Trả lời
$A=$ $\frac{1}{1.2}$+ $\frac{1}{2.3}$+$\frac{1}{3.4}$+…+$\frac{1}{19.20}$
=1-$\frac{1}{2}$+$\frac{1}{2}$$\frac{1}{3}$+…+$\frac{1}{19}$-$\frac{1}{20}$
= 1-$\frac{1}{20}$
= $\frac{20}{20}$-$\frac{1}{20}$
= $\frac{19}{20}$
$A = \dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + …. + \dfrac{1}{19.20}$
$A = 1 – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{4} + …. + \dfrac{1}{19} – \dfrac{1}{20}$
$A = 1 – \dfrac{1}{20}$
$A = \dfrac{19}{20}$
Công thức chung:
$\dfrac{a}{1 + (a+1)} + \dfrac{a}{2 + (a+ 2)} + \dfrac{a}{3 + (a+ 3)} + …. + \dfrac{a}{n +(a+ n)}$
$=\dfrac{1}{1} – \dfrac{1}{a} + \dfrac{1}{2} – \dfrac{1}{a+1} + …. + \dfrac{1}{n} – \dfrac{1}{a+n}$