`Answer:`

\(\left(x-5\right)^5=\left(x-5\right)^{15}\)

\(\Leftrightarrow\left(x-5\right)^5=\left(x-5\right)^{10}.\left(x-5\right)^5\)

\(\Leftrightarrow\left(x-5\right)^{10}=1\)

\(\Leftrightarrow x-5=1\)

\(\Leftrightarrow x=6\)

`Answer:`

Bạn bổ sung thêm trường hợp `x-5=-1<=>x=4` giúp mình nhé.

`Answer:`

\(S=1+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)

\(=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)\)

Ta thấy:

\(\frac{1}{13}< \frac{1}{12}\)

\(\frac{1}{14}< \frac{1}{12}\)

\(\frac{1}{15}< \frac{1}{12}\)

\(\Rightarrow\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}\)

\(\Rightarrow\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{4}\text{(*)}\)

Ta thấy:

\(\frac{1}{61}< \frac{1}{60}\)

\(\frac{1}{62}< \frac{1}{60}\)

\(\frac{1}{63}< \frac{1}{60}\)

\(\Rightarrow\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}\)

\(\Rightarrow\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{20}\text{(**)}\)

Từ (*)(**)\(\Rightarrow S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}\)

\(\Rightarrow S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)

ai bt

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