Sum of infinitesimals and sum of infinitesimals The sum of infinitesimals is not necessarily infinitesimal. It may be infinitesimal, infinitesimal or bounded However, the sum of finite infinitesimals is infinitesimal. I am a little confused about these two problems. Can you give me a simple example to explain them?
When n approaches infinity,
(1) 1 / N + 1 / N + 1 / N +. + 1 / N (n) = 1 (bounded);
(2) 1 / N ^ 2 + 1 / N ^ 2 +. + 1 / N ^ 2 (n) = 1 / N (infinitesimal);
(3) 1 / N + 1 / N +. + 1 / N (n ^ 2) = n (infinity)
Let X - > 0, ax & # 178; + BX + c-cosx be infinitesimal of higher order than X & # 178;, and find the values of constants a, B, C?
The Taylor expansion method is not used
List LIM (AX & # 178; + BX + c-cosx) / X & # 178; = 0 when x tends to 0, the denominator of the equation x & # 178; tends to 0, and the right limit is 0, then the equation can be understood as a molecule divided by an infinitesimal quantity, the result is 0, because x tends to 0 and is not equal to 0, so multiply both sides of the equation by X & # 178;, the denominator is removed, and the right