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?

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