Toán Lớp 4: Tính nhanh
1/3 + 1/15 + 1/35 + 1/63 + 1/99
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Toán Lớp 4: Tính nhanh
1/3 + 1/15 + 1/35 + 1/63 + 1/99
Comments ( 2 )
Đặt A= 1/3+ 1/15 + 1/35 + 1/63 +1/99
2A= 2/1×3 + 2/3×5 + 2/5×7 + 2/7×9 + 2/9×11
2A= 1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11
2A= 1-1/11
2A= 10/11
⇒ A= 10/11 ÷ 2
A= 5/11
Vậy 1/3 + 1/15 + 1/35 + 1/63 + 1/99 = 5/11
$\dfrac{1}{3}$ + $\dfrac{1}{15}$ + $\dfrac{1}{35}$ + $\dfrac{1}{63}$ + $\dfrac{1}{99}$
= $\dfrac{1}{1×3}$ + $\dfrac{1}{3×5}$ + $\dfrac{1}{5×7}$ + $\dfrac{1}{7×9}$ +
$\dfrac{1}{9×11}$
= $\dfrac{1}{2}$ x ( $\dfrac{2}{1×3}$ + $\dfrac{2}{3×5}$ + $\dfrac{2}{5×7}$+$\dfrac{2}{9×11}$)
= $\dfrac{1}{2}$ x ( 1-$\dfrac{1}{3}$+$\dfrac{1}{3}$-$\dfrac{1}{5}$ + .. + $\dfrac{1}{9}$ – $\dfrac{1}{11}$ )
= $\dfrac{1}{2}$ x ( 1 – $\dfrac{1}{11}$)
= $\dfrac{1}{2}$ x $\dfrac{10}{11}$
= $\dfrac{5}{11}$