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If 1 2020 + 2 2019 + 3 2018 + . . . . . . . . . + 2020 1 = 2020 × 2021 × k , then the value of k 100 is equal to

Correct answer

3.37

Step-by-step solution

t r = r 2021 - r S = ∑ r = 1 2020 t r = ∑ r = 1 2020 r 2021 - r = 2021 ∑ r = 1 2020 r - ∑ r = 1 2020 r 2 = 2021 × 2020 × 2021 2 - 2020 × 2021 × 4041 6 = 2021 × 2020 2 2021 - 4041 3 = 2020 × 2021 2 × 67 4 = 2020 × 2021 × 33 7 ⇒ k = 337 ⇒ k 100 = 3.3 7

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