Chứng minh rằng A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1324 < 1/2 09/08/2021 Bởi Arya Chứng minh rằng A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1324 < 1/2
Đáp án + Giải thích các bước giải: – Nguyễn Phúc Thăng Long – Xin Hay Nhất A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1324 A = 1/2.2+1/4.4+1/6.6+1/8.8+1/10.10+1/12.12+1/14.14+1/16.16+1/18.18 A = 1/2 – 1/2 + 1/4 – 1/4 + 1/8 – 1/8 +1/10 – 1/10 + … + 1/18 – 1/18 A = 0 Vì 0 < 1/2 vậy : A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1324 Bình luận
1/4 = 1/(2.2) < 1/(1.2) = 1/2 – 1/4 1/16 < 1/(2.4) = 1/4 – 1/8 1/36 < 1/(4.6) = 1/8 – 1/12 1/64 < 1/(6.8) = 1/12 – 1/16 1/100 < 1/(8.10) = 1/16 – 1/20 1/144 < 1/(10.12) = 1/20 – 1/24 1/196 < 1/(12.14) = 1/24 – 1/28 1/256 < 1/(14.16) = 1/28 – 1/32 1/324 < 1/(16.18) = 1/32 – 1/36 ⇒ 1/4 + 1/16 + ……+ 1/100 + 1/144 + 1/196 +1/256+1/324< 1/2 – 1/36 < 1/2 (đpcm) Bình luận
Đáp án + Giải thích các bước giải:
– Nguyễn Phúc Thăng Long
– Xin Hay Nhất
A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1324
A = 1/2.2+1/4.4+1/6.6+1/8.8+1/10.10+1/12.12+1/14.14+1/16.16+1/18.18
A = 1/2 – 1/2 + 1/4 – 1/4 + 1/8 – 1/8 +1/10 – 1/10 + … + 1/18 – 1/18
A = 0
Vì 0 < 1/2
vậy : A = 1/4+1/16+1/36+1/64+1/100+1/144+1/196+1/256+1324
1/4 = 1/(2.2) < 1/(1.2) = 1/2 – 1/4
1/16 < 1/(2.4) = 1/4 – 1/8
1/36 < 1/(4.6) = 1/8 – 1/12
1/64 < 1/(6.8) = 1/12 – 1/16
1/100 < 1/(8.10) = 1/16 – 1/20
1/144 < 1/(10.12) = 1/20 – 1/24
1/196 < 1/(12.14) = 1/24 – 1/28
1/256 < 1/(14.16) = 1/28 – 1/32
1/324 < 1/(16.18) = 1/32 – 1/36
⇒ 1/4 + 1/16 + ……+ 1/100 + 1/144 + 1/196 +1/256+1/324< 1/2 – 1/36 < 1/2
(đpcm)