Find the sum of the infinite series 1+43+932+1633+……..∞

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112

132

answer is D.

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Detailed Solution

This is clearly not an AGP series, since 1, 4,9, 16…are not in A.P. However their successive difference 4-1=3, 9-4=5, 169=7,… are in A.P. Let S∞=1+43+932+1633+…..∞(1)13S∞=13+432+933+…∞−(2) Substracting (2) from (1) 23S∞=1+33+532+733+….+∞13⋅23S∞=13+332+533+…..+∞ On subtracting 49S∞=1+23+232+….+∞=1+231+13+132+…..+∞=1+231−11−13=2∴S∞=2×94=92

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