4S = 1 / 30+0 + 1/3(1)+(1) +.............+∞
= 1/(1-1/32 )
= 9/8
Find the sum of this infinite series
\sum_{0\leq i\neq j\leq \infty}{\left(3^{-i}\times 3^{-j})}
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16 Answers
341to get some idea on how to proceed, look at the derivation of the sum of divisors of a number.
1sir is
S= 9/4 correct .
using sum of infinite terms of a G.P
keeping i =0 varying j from o to ∞
keepint i=1 and varying j from o to ∞
i.e
S= 1/30{ 1/30+1/31+...+1/3∞}
+1/31{ 1/30+1/31+...+1/3∞}
+...
62anirudh you have also missed out something.. see more closely..
1sir
i≠j .
thus from my solution i have to subtract those cases of
i=j
106if anirudh's calc is correct,
the final ans is S - [(1/30)2 + (1/31)2 + ...]
= 9/4 - 11-1/9
= 9/4 - 9/8
= 9/8
verification of anirudhs calc
S = (1/30 + 1/31 + 1/32 + ... )2
= (11-1/3)2
= 9/4
1S =
9/4-9/8
= 9/8
sir this answer is same as @uttara answers so i got a little Confused