1 / M + 1), 2 / M + 2),. M / M + 1 I don't understand the answer

1 / M + 1), 2 / M + 2),. M / M + 1 I don't understand the answer

1/(m+1)+2/(m+1)+… +M / (M + 1) = (1 + 2 +... + m) / (1 + m) = m (1 + m) / [2 (1 + m)] = m / 2  s (m) = 1 / 2 + 1 / 3 + 2 / 3 +... + 1 / (M + 1) +... + m / (M + 1) = 1 / 2 + 2 / 2 + 3 / 2 +... + m / 2 = (1 + 2 +... + m) / 2 = m (1 + m) / 4 terms n = 1 + 2 +... + k = [K (K + 1)] / 2 when k = 8, n = 36 when k = 9, n = 45

Sequence summation 3 + 5 + 7 +... + 2N-1

The sum of arithmetic sequence can be: (3 + 2n-1) * (n-1) / 2 = n ^ 2-1

It is shown that (n + 7) ^ 2 (N-5) ^ 2 can be divided by 24

(n+7)² - (n-5)² = (n+7+n-5)(n+7-n+5)
= (2n+2)*12
= (n+1)*24
Therefore, (n + 7) ² - (N-5) ² can be divisible by 24