Question

Find the sum of 1+(1/3)+(1/6)+(1/10)+(1/15)+...up to 20 terms​

Answer 1

Answer:

Let series S= 1/1+1/3+1/6+1/10+1/15+…….

S can be rewritten as

S = 2 * (1/2+1/6+1/12+1/20+1/30+……..)

Now, let’s consider each term

1/2 = 1 - 1/2

1/6 = 1/2 - 1/3

1/12 = 1/3 - 1/4

1/20 = 1/4 - 1/5

1/30 = 1/5 - 1/6

Thus,

S = 2 * (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 +………)