Đáp án: -$\frac{101}{200}$
Giải thích các bước giải:
A = ($\frac{1}{2^{2}}$ - 1)($\frac{1}{3^{2}}$ - 1)($\frac{1}{4^{2}}$ - 1)...($\frac{1}{99^{2}}$ - 1)($\frac{1}{100^{2}}$ - 1)
= ($\frac{1}{2}$ - 1)($\frac{1}{2}$ + 1)($\frac{1}{3}$ - 1)($\frac{1}{3}$ + 1)($\frac{1}{4}$ - 1)($\frac{1}{4}$ + 1)...($\frac{1}{99}$ - 1)($\frac{1}{99}$ + 1)($\frac{1}{100}$ - 1)($\frac{1}{100}$ + 1)
= (-$\frac{1}{2}$).(-$\frac{2}{3}$).(-$\frac{3}{4}$)...(-$\frac{98}{99}$).(-$\frac{99}{100}$).$\frac{3}{2}$.$\frac{4}{3}$.$\frac{5}{4}$...$\frac{100}{99}$ .$\frac{101}{100}$
= -$\frac{1}{100}$.$\frac{101}{2}$
= -$\frac{101}{200}$
