Sum the following series
(i)1 + 
+ 
+ 
+ ........ to n terms.
(ii) 1 + 
+ 
+ 
+ 
+ ..... to infinity.
Text Solution
Verified by Experts(ii) (i); (ii) (i)
(i) 4 – 
(ii) 
Sol. (i) 1 + 
+ 
+ ........... n terms
T n = 
S = 1 + 
+ 
+............+ 
...(i)
S = 
+ 
+ ..........+ 
+ 
...(ii)
(i) – (ii) we get
S = [1+ 
+ 
+.........+ 
] – 
S = 
– 
⇒ S = 4 –4 
– 
; S = 4 – 
(ii) S = 1 + 
+ 
+ 
+ 
+ ........ ∞ ..... (i)
S = 
+ 
+ 
+ ........ ∞ ..... (ii)
(i) – (ii), we get
S = 1 + 
+ 
+ 
+ ........ ∞ ⇒ 
S = 
⇒ S = 
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