sum of 1/1x2, 1/2×3, 1/3×4,........1/28×29, 1/29×30

Question

Sum of 1/1×2, 1/2×3, 1/3×4,.......1/28×29, 1/29×30

Answer 1

Each term could be written (n+1)/n where 1≤n≤29, where n is an integer (whole number).

The sum can be expressed as ∑₁²⁹(n+1)/n=∑₁²⁹(​1+1/n)=29+∑₁²⁹​(​1/n).

So we need the sum of the reciprocals of natural numbers up to 29.

This sum is 3.9616538 approx. So the sum is 32.9616538 approx.