bạn giải dùm mình bài này nhé Tìm x biết: 2+2+2² +2³+2⁴+...+2²⁰¹⁴=2^x.  Ai giúp mình giải bài này với

1/4+1/16=1\20

1\20+1/36=1/56

1/56+1/64=1\120

1/120+1/100=1/220

1/220+1/44=1/264

1/264+1/196=1/460

1/460+1/256=1/716

suy ra:1/716 ko phải số TN

Ta có : \(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+...+\frac{1}{256}>0\)

\(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}+\frac{1}{256}\)

\(A< \frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}+\frac{1}{49}+\frac{1}{64}\)\(+\frac{1}{81}+\frac{1}{100}+\frac{1}{121}+\frac{1}{144}+\frac{1}{169}+\frac{1}{196}+\frac{1}{225}+\frac{1}{256}\)

\(A< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{15\cdot16}\)

\(A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{15}-\frac{1}{16}\)

\(A< 1-\frac{1}{16}< 1\)

\(\Rightarrow0< A< 1\)

=> A ko là số tự nhiên

\(Đ\text{ặt }S=\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+....+\frac{1}{10000}\)

\(S=\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}\)

\(S=\frac{1}{2^2}\cdot\left(1+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\right)\)

Ta có :

\(\frac{1}{2^2}< \frac{1}{1\cdot2};\text{ }\frac{1}{3^2}< \frac{1}{2\cdot3};\text{ }...;\text{ }\frac{1}{50^2}< \frac{1}{49\cdot50}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{49\cdot50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 1\Rightarrow1+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< 1+1=2\)

\(\Rightarrow\frac{1}{2^2}\left(1+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\right)< \frac{1}{2^2}\cdot2\)

\(\Rightarrow S< \frac{1}{2}\) (ĐPCM)

Đặt \(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+....+\frac{1}{10000}\)

\(\Rightarrow A=\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{100^2}\)

\(\Rightarrow4A=1+\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{50^2}\)

\(\Rightarrow4A< 1+\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{49.50}\)

\(\Rightarrow4A=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(\Rightarrow4A< 2-\frac{1}{50}< 2\)

\(\Rightarrow4A< 2\Rightarrow A< \frac{2}{4}=\frac{1}{2}\)

=>a<1/2

kho lm giup minh voi

Bạn tham khảo nhé 

A=14 +116 +136 +164 +1100 +1144 +1196 =122 +142 +162 +182 +1102 +1122 +1142 

2A=222 +242 +262 +282 +2102 +2122 +2142 

2A<12 +22.4 +24.6 +26.8 +28.10 +210.12 +212.14 

2A<12 +12 −14 +14 −16 +16 −18 +18 −110 +110 −112 +112 −114 

2A<12 +12 −114 

2A<1−114 

2A<1314 

A<1328 <1428 =12  ( đpcm ) 

Vậy A<12 

Chúc bạn học tốt ~

Đặt \(A\)\(=\frac{1}{2^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)

Ta có: \(A< \frac{1}{2^2-1}+\frac{1}{4^2-1}+...+\frac{1}{100^2-1}\)

 \(A< \frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{99.101}\)

\(A< \frac{1}{2}.\left(1-\frac{1}{101}\right)\)

\(A< \frac{1}{2}.1\)( VÌ \(1-\frac{1}{101}< 1\))

\(A< \frac{1}{2}\)

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