What is the Infinite sum of Series 1/1 + 1/3 + 1/6 + 1/10 + 1/15 + ?

Linear equaation, Irrational Number, Property of Rational Number

Question:-What is the infinite sum of the series 1/1 + 1/3 + 1/6 + 1/10 + 1/15 + ?

Answer:-  Let Tn represents the n-th term in this series.

T1 = 1/(1)

T2 =,1/(1+2)

T3 = 1/(1+2+3)

T4 = 1/(1+2+3+4)

T5 = 1/(1+2–3+4+5) and so on

-> Tn = 1/(1+2+3+……..+n)

= 1/ [ n(n+1)/2 ] = 2/n(n+1)

Tn = 2 / [ n(n+1) ]

= 2 * [ (1/n) - 1/(n+1) ]

If you add all the terms you will get >

2 * [ 1/1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 +1/4 - 1/5 + 1/5 - 1/6 +…….]

= 2  Answer

Solve by Raj