Question

chứng minh rằng: 1/2^2+1/3^2+1/4^2+....+1/50^2<1

Answer 1

\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+...+\(\frac{1}{50^2}\)<1

ta có \(\frac{1}{2^2}\)<\(\frac{1}{1.2}\)

       \(\frac{1}{3^2}\)<\(\frac{1}{2.3}\)

    ..........................

    \(\frac{1}{50^2}\)<\(\frac{1}{49.50}\)

ta được \(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+...+\(\frac{1}{49.50}\)

          =>1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-...-\(\frac{1}{49}\)+\(\frac{1}{49}\)-\(\frac{1}{50}\)

          =>1-\(\frac{1}{50}\)<1 nên\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+...+\(\frac{1}{50^2}\)<1

vậy ...........................