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

Question

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

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3 tháng 2021-09-08T17:31:48+00:00 2 Answers 11 views 0

1. $\text{K=$\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}$}$

2. 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