A= 7/4 + 17/9 + 31/16 +...+4999/2500
Chứng minh A>97
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NV
1
23 tháng 5 2019
\(A=\frac{7}{4}+\frac{17}{9}+\frac{31}{16}+....+\frac{4999}{2500}\)
\(A=\frac{3+4}{2^2}+\frac{8+9}{3^2}+\frac{15+16}{4^2}+....+\frac{2499+2500}{50^2}\)
\(A=\frac{\left(4-1\right)+4}{2^2}+\frac{\left(9-1\right)+9}{3^2}+\frac{\left(16-1\right)+16}{4^2}+...+\frac{\left(2500-1\right)+2500}{50^2}\)
\(A=\frac{4+4-1}{2^2} +\frac{9+9-1}{3^2}+\frac{16+16-1}{4^2}+...+\frac{2500+2500-1}{50^2}\)
\(A=\frac{2^2+2^2-1}{2^2}+\frac{3^2+3^2-1}{3^2}+\frac{4^2+4^2-1}{4^2}+...+\frac{50^2+50^2-1}{50^2}\)
\(A=\frac{2\times2^2-1}{2^2}+\frac{2\times3^2-1}{3^2}+\frac{2\times4^2-1}{4^2}+...+\frac{2\times50^2-1}{50^2}\)
\(A=\left(\frac{2\times2^2}{2^2}-\frac{1}{2^2}\right)+\left(\frac{2\times3^2}{3^2}-\frac{1}{3^2}\right)+\left(\frac{2\times4^2}{4^2}-\frac{1}{4^2}\right)+...+\left(\frac{2\times50^2}{50^2}-\frac{1}{50^2}\right)\)
\(A=\left(\frac{2\times2^2}{2^2}+\frac{2\times3^2}{3^2}+\frac{2\times4^2}{4^2}+...+\frac{2\times50^2}{50^2}\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
\(A=\left(2+2+2+...+2\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
49 số 2
\(A=98-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
\(>98-\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{49\times50}\right)\)
\(=98-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\)
\(=98-\left(1-\frac{1}{50}\right)\)
\(=98-1+\frac{1}{50}\)
\(=97+\frac{1}{50}>97\)
\(\Rightarrow A>97\left(ĐPCM\right)\)
Nhớ tích cho mk nha thank for watching
BT
0
BT
0
NP
6
BT
0
BT
0
TL
6
4 tháng 3 2017
b) 78.(31+24+17)+22.72
= 78.82+22.72
=78.10+72.(78+22)
=780+7200
=7980
k minh nha ninh dang can no gap