$vu$
Đáp án+Giải thích các bước giải:
a, Ta có : a = $\dfrac{1}{1.101}$ + $\dfrac{1}{2.102}$ + $\dfrac{1}{3.103}$ +...+ $\dfrac{1}{10.110}$
= $\dfrac{1}{100}$.(1-$\dfrac{1}{100}$+$\dfrac{1}{2}$-$\dfrac{1}{102}$+$\dfrac{1}{3}$-$\dfrac{1}{103}$+...+$\dfrac{1}{10}$-$\dfrac{10}{110}$)
= $\dfrac{1}{100}$ .[(1+$\dfrac{1}{2}$+$\dfrac{1}{3}$+...+$\dfrac{1}{10}$)-($\dfrac{1}{100}$+$\dfrac{1}{102}$+$\dfrac{1}{103}$+...+$\dfrac{1}{110}$)]
b = $\dfrac{1}{1.11}$+$\dfrac{1}{2.12}$+$\dfrac{1}{3.13}$+...+$\dfrac{1}{100.110}$
= $\dfrac{1}{10}$.(1-$\dfrac{1}{11}$+$\dfrac{1}{2}$-$\dfrac{1}{12}$+$\dfrac{1}{3}$-$\dfrac{1}{13}$+...+$\dfrac{1}{100}$-$\dfrac{1}{110}$)
= $\dfrac{1}{10}$.[(1+$\dfrac{1}{2}$+$\dfrac{1}{3}$+...+$\dfrac{1}{100}$)-($\dfrac{1}{11}$+$\dfrac{1}{12}$+$\dfrac{1}{13}$+...+$\dfrac{1}{110}$)]
Suy ra: b = 10a. Từ đó tìm được x = 10.
chúc bạn học tốt
