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If S = 1 25 + 2 24 + 3 23 + . . . . . . + 24 2 + 25 1 , then the value of S 900 is equal to

Correct answer

3.25

Step-by-step solution

S = ∑ r = 1 25 r 26 - r = 26 ∑ r = 1 25 r - ∑ r = 1 25 r 2 = 26 × 25 × 26 2 - 25 × 26 × 51 6 = 25 × 26 2 26 - 51 3 = 25 × 26 13 2 × 9 ⇒ S 900 = 13 4 = 3.2 5

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