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JEE Main202226 Jun 2022Morning ShiftMathematicsSequences and SeriesActual

Let A = ∑ i = 1 10 ∑ j = 1 10 min i , j and B = ∑ i = 1 10 ∑ j = 1 10 max i , j . Then A + B is equal to _____.

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Step-by-step solution

A = ∑ i = 1 10 ∑ j = 1 10 min i , j B = ∑ i = 1 10 ∑ j = 1 10 max i , j A = ∑ j = 1 10 min i , 1 + min j , 2 + … min i , 10 = 1 + 1 + 1 + … + 1 ⏟ 19   times   + 2 + 2 + 2 … + 2 ⏟ 17   times   + 3 + 3 + 3 … + 3 ⏟ 15   times     + . . . B = ∑ j = 1 10 max i , 1 + max j , 2 + … max i , 10 = 10 + 10 + … + 10 ⏟ 19   times   + 9 + 9 + … + 9 ⏟ 17   times   + . .

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