Chứng minh: 1/4+1/16+1/36+1/64+1/100+1/144+1/196 < 1/2 Đang cần gấp ạ mau lên nhaa. chiều ni mk thi ròi 09/10/2021 Bởi Sarah Chứng minh: 1/4+1/16+1/36+1/64+1/100+1/144+1/196 < 1/2 Đang cần gấp ạ mau lên nhaa. chiều ni mk thi ròi
Đáp án: Giải thích các bước giải: Đặt A= 1/4+1/16+1/36+1/64+1/100+1/144+1/196 = 1/2^2+ 1/4^2+ 1/6^2+….+ 1/16^2 = 1/2^2.( 1+ 1/2^2+ 1/3^2+…+ 1/8^2) Ta có 1+ 1/2^2+ 1/3^2+…+ 1/8^2< 1+ 1/1.2+ 1/2.3+….7.8= 1+ 1-1/2+ 1/2- 1/3+….+ 1/7- 1/8 = 2- 1/8< 2 Nên ( 1+ 1/2^2+ 1/3^2+…+ 1/8^2)< 2 => A< 1/2^2 nhân 2= 1/2 Vậy A< 1/2 Bình luận
TL: $\frac{1}{4}$ $+ \frac{1}{16}$ $+ \frac{1}{64}$ $+ \frac{1}{100}$ $+ \frac{1}{144}$ $+\frac{1}{196}$ $< \frac{1}{2}$ $= \frac{1}{4}$ $+ \frac{1}{16}$ $+ \frac{1}{64}$ $+ \frac{1}{100}$ $+ \frac{1}{144}$ $+\frac{1}{196}$ $< \frac{1}{2^2 – 1 }$ $+ \frac{1}{4^2 – 1}$ $+ \frac{1}{6^2 – 1}$ $+ … +\frac{1}{14^2 – 1}$ $= \frac{1}{1.3}$ $\frac{1}{3.5}$ $\frac{1}{5.7}$ $+ … +\frac{1}{13.15}$ $=\frac{1}{2}$ $( 1 – \frac{1}{3}$ $+\frac{1}{3}$ $- $ …. $ – \frac{1}{13}$ $-\frac{1}{13}$ $+\frac{1}{15} )$ $=\frac{1}{2}( 1 – $ $\frac{1}{15})$ $<\frac{1}{2}$ $Vậy…$ Bình luận
Đáp án:
Giải thích các bước giải:
Đặt A= 1/4+1/16+1/36+1/64+1/100+1/144+1/196
= 1/2^2+ 1/4^2+ 1/6^2+….+ 1/16^2
= 1/2^2.( 1+ 1/2^2+ 1/3^2+…+ 1/8^2)
Ta có 1+ 1/2^2+ 1/3^2+…+ 1/8^2< 1+ 1/1.2+ 1/2.3+….7.8= 1+ 1-1/2+ 1/2- 1/3+….+ 1/7- 1/8
= 2- 1/8< 2
Nên ( 1+ 1/2^2+ 1/3^2+…+ 1/8^2)< 2
=> A< 1/2^2 nhân 2= 1/2
Vậy A< 1/2
TL:
$\frac{1}{4}$ $+ \frac{1}{16}$ $+ \frac{1}{64}$ $+ \frac{1}{100}$ $+ \frac{1}{144}$ $+\frac{1}{196}$ $< \frac{1}{2}$
$= \frac{1}{4}$ $+ \frac{1}{16}$ $+ \frac{1}{64}$ $+ \frac{1}{100}$ $+ \frac{1}{144}$ $+\frac{1}{196}$ $< \frac{1}{2^2 – 1 }$ $+ \frac{1}{4^2 – 1}$ $+ \frac{1}{6^2 – 1}$ $+ … +\frac{1}{14^2 – 1}$
$= \frac{1}{1.3}$ $\frac{1}{3.5}$ $\frac{1}{5.7}$ $+ … +\frac{1}{13.15}$
$=\frac{1}{2}$ $( 1 – \frac{1}{3}$ $+\frac{1}{3}$ $- $ …. $ – \frac{1}{13}$ $-\frac{1}{13}$ $+\frac{1}{15} )$
$=\frac{1}{2}( 1 – $ $\frac{1}{15})$ $<\frac{1}{2}$
$Vậy…$