InterviewSolution
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InterviewSolution
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If the surm of the first ten terms of the series,`(1 3/5)^2+(2 2/5)^2+(3 1/5)^2+4^2+(4 4/5)^2+........`, is `16/5m` ,then m is equal toA. 102B. 101C. 100D. 99 |
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Answer» Correct Answer - B Let S be the sum of the following series. `(1(3)/(5))^(2)+(2(2)/(5))^(2)+(3(1)/(5))^(2)+4^(2)+ . . . . .` upto 10 terms i.e. `S=((8)/(5))^(2)+((12)/(5))^(2)+((16)/(5))^(2)+((20)/(5))^(2)+((24)/(5))^(2)+ . . . . . .` upto 10 terms `rArr" "S=underset(r=1)overset(10)sum{(8+4(r-1))/(5)}^(2)` `rArr" "S=(16)/(25)underset(r=1)overset(10)sum(r+1)^(2)` `rArr" "S=(16)/(25){underset(r=0)overset(10)sum(r+1)^(2)-1^(2)}` `rArr" "(16)/(25)m=(16)/(25){(11xx12xx23)/(6)-1}" "{:[becauseS=(16)/(5)m"(given)"]:}` `rArr" "m=(1)/(5)(22xx23-1)rArrm=101` |
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