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The sum of the infinite series is
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a
4/2
b
9/2
c
4/9
d
1
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Correct option is B
This is clearly not an arithmetico-geometric series,since 1, 4, 9, '16, ... are not in AP. However, their successive differences (4 - 1), (9 - 4), (16 - 9) ,... are in AP.LetS∞=1+43+932+1633+…∞13S∞=13+432+933+…∞On subtraction, we get23S∞=1+33+532+733+…∞⇒13⋅23S∞=13+332+533+…∞ multiplying both sides by 13On subtracting the two series, we get49⋅S∞=1+23+232+233+…∞=1+231+13+132+…∞=1+23×11−13=2∴ S∞=2×94=92Similar Questions
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