\(S=1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+....+\dfrac{1}{100^2}< 1+\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)
\(=1+\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1+1-\dfrac{1}{100}\)
\(=2-\dfrac{1}{100}< 2\)
\(\Rightarrow S< 2\left(đpcm\right)\)
Vậy S < 2
ChoM=1+1/2+1/3+...+1/[(2^100)-1]
Cm M<50
cho A= 1/2 2/2^2 3/2^3 .... 99/2^99 100/2^100 so sánh A với 2
1)tính
S=2^2+4^2+6^2...+20^2 biet 1^2+2^2+3^2+...+10^2=385
2)tính
A=2^0+2^1+2^3+...+2^100
CM: \(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
so sánh A= (\(\dfrac{1}{2^2}\) -1) (\(\dfrac{1}{3^2}\) -1)..........(\(\dfrac{1}{100^2}\) -1) VỚI -\(\dfrac{1}{2}\)
\(A=\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+.+\dfrac{99}{2^{99}}+\dfrac{100}{2^{100}}.\)So sánh A với 2
Cho A = \(\left(\dfrac{1}{2^2}-1\right).\left(\dfrac{1}{3^2}-1\right).\left(\dfrac{1}{4^2}-1\right)....\left(\dfrac{1}{100^2}-1\right)\)
So sánh A với \(\dfrac{-1}{2}\)
Cho A = \(\left(\dfrac{1}{2^2}-1\right).\left(\dfrac{1}{3^2}-1\right).\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{100^2}-1\right)\)
So sánh A với \(-\dfrac{1}{2}\)
A=\(\left(\dfrac{1}{2^2}-1\right).\left(\dfrac{1}{3^2}-1\right).\left(\dfrac{1}{4^2}-1\right).....\left(\dfrac{1}{100^2}-1\right)\)
So sánh A voi \(\dfrac{1}{2}\)
