Ask for the sum of the reciprocal sequence of natural numbers, 1+1/2+1/3+1/4+ … +Sum of reciprocal sequence of 1 / n natural numbers And 1 + 1 / (2 * 2) + 1 / (3 * 3) + 1 / (4 * 4) + +Sum of reciprocal square sequence of 1 / (n * n) natural number ～ Many people say it can't be solved Another point I ask is the sum of the first n terms, not the limit. But others say it's →∞ I don't understand why the sequence 2481632... 2yn is also →∞, but the sum of the first n terms can be obtained?

Ask for the sum of the reciprocal sequence of natural numbers, 1+1/2+1/3+1/4+ … +Sum of reciprocal sequence of 1 / n natural numbers And 1 + 1 / (2 * 2) + 1 / (3 * 3) + 1 / (4 * 4) + +Sum of reciprocal square sequence of 1 / (n * n) natural number ～ Many people say it can't be solved Another point I ask is the sum of the first n terms, not the limit. But others say it's →∞ I don't understand why the sequence 2481632... 2yn is also →∞, but the sum of the first n terms can be obtained?

At 20:48 on June 10, a series of reciprocal natural numbers is called harmonic series. People have studied it for hundreds of years. But so far, there is no summation formula for it, only its approximate formula (when n is very large)
1 + 1 / 2 + 1 / 3 +. + 1 / N ≈ lnn + C (C = 0.57722. An irrational number, called Euler initial, is specially used for Harmonic Series)
People tend to think that it does not have a simple summation formula
However, it is not because it is divergent that there is no summation formula. On the contrary, for example, the arithmetic sequence is divergent, and the arithmetic sequence whose absolute value of common ratio is greater than 1 is also divergent. They all have summation formulas