Đáp án:
Giải thích các bước giải:
C = $\frac{1}{12}$ + $\frac{1}{30}$ + $\frac{1}{56}$ +...+ $\frac{1}{2652}$
= $\frac{1}{3×4}$ + $\frac{1}{5×6}$ + $\frac{1}{7×8}$ +...+ $\frac{1}{51×52}$
< $\frac{1}{2×4}$ + $\frac{1}{4×6}$ + $\frac{1}{6×8}$ +...+ $\frac{1}{50×52}$
=$\frac{1}{2}$($\frac{1}{2}$ - $\frac{1}{4}$ + $\frac{1}{4}$ - $\frac{1}{6}$ +...+ $\frac{1}{50}$ - $\frac{1}{52}$)
= $\frac{1}{2}$( $\frac{1}{2}$ - $\frac{1}{52}$) < $\frac{1}{2}$ × $\frac{1}{2}$ = $\frac{1}{4}$
⇒ C < $\frac{1}{4}$ (đpcm)
