Tính nhanh K=1/4+1/12+1/24+1/40+1/60+1/84+1/112 giải chi tiet cho minh nhe

$\text{K=$\dfrac{1}{4}$ +$\dfrac{1}{12}$+...+ $\dfrac{1}{112}$}$

$\text{⇒K=$\dfrac{1}{4}$(1+ $\dfrac{1}{3}$+...+ $\dfrac{1}{28}$ )}$

$\text{Xét 1+ $\dfrac{1}{3}$+...+ $\dfrac{1}{28}$}$

$\text{⇒1>1+$\dfrac{1}{28}$}$

$\text{⇒$\dfrac{1}{3}$>$\dfrac{1}{28}$}$

$\text{⇒$\dfrac{1}{28}$=$\dfrac{1}{28}$  (Có 7 số hạng)}$

$\text{nên 1+ $\dfrac{1}{3}$+...+ $\dfrac{1}{28}$>$\dfrac{1}{28}$×7=$\dfrac{1}{4}$}$

$\text{Do đó:K=$\dfrac{1}{4}$(1+ $\dfrac{1}{3}$+...+ $\dfrac{1}{28}$ )>$\dfrac{1}{4}$×$\dfrac{1}{4}$=$\dfrac{1}{16}$}$

$\text{Vậy K>$\dfrac{1}{16}$}$

Đáp án:

 7/16

Giải thích các bước giải:

K=(28/112 + 1/112) + (2/24 + 1/24) + (6/240 + 4/240) + 1/84

K=29/112 + 3/24 + 10/240 + 1/84

K=29/112 + 30/240 + 10/240 + 1/84

K=29/112 + 40/240 + 1/84

K=29/112 + 1/6 + 1/84

K=29/112 + 14/84 + 1/84

K=29/112 + 15/84

K=7/16