Ta có:

$\dfrac{1}{2^{2}}$ $<$ $\dfrac{1}{1.2}$

$\dfrac{1}{3^{2}}$ $<$ $\dfrac{1}{2.3}$

$\dfrac{1}{4^{2}}$ $<$ $\dfrac{1}{3.4}$

$\dfrac{1}{5^{2}}$ $<$ $\dfrac{1}{5.6}$

...........

$\dfrac{1}{8^{2}}$ $<$ $\dfrac{1}{7.8}$

⇒ $B$ $<$ $\dfrac{1}{1.2}$ $+$ $\dfrac{1}{2.3}$ $+$ ....+ $\dfrac{1}{7.8}$

⇒ $B$ $<$ $1$ $-$ $\dfrac{1}{2}$ $+$ $\dfrac{1}{2}$ $-$ $\dfrac{1}{3}$ $+$.....+ $\dfrac{1}{7}$ $-$ $\dfrac{1}{8}$

⇒ $B$ $<$ $1$ $-$ $\dfrac{1}{8}$ $<$ $1$ ( Vì $\dfrac{1}{8}$ $>$ $0$)

Vậy $B$ $<$ $1$

Chúc me học tốt!

Đáp án:

Giải thích các bước giải:

 Ta có:

$\dfrac{1}{2^{2}}< \dfrac{1}{1. 2}; \dfrac{1}{3^{2}}< \dfrac{1}{2. 3};...; \dfrac{1}{8^{2}}< \dfrac{1}{7.8}$

$⇒ \dfrac{1}{2^{2}}+ \dfrac{1}{3^{2}}+....+ \dfrac{1}{8^{2}}< \dfrac{1}{2. 3};...; \dfrac{1}{8^{2}}< \dfrac{1}{7.8}$

$⇒ \dfrac{1}{2^{2}}+ \dfrac{1}{3^{2}}+....+ \dfrac{1}{8^{2}}< 1- \dfrac{1}{8}< 1$

$⇒ \dfrac{1}{2^{2}}+ \dfrac{1}{3^{2}}+....+ \dfrac{1}{8^{2}}< 1$