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
