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If 20 19 + 2 21 20 18 + 3 21 2 20 17 + . . . + 20 21 19 = k 20 19 , then k is equal to _____.

Correct answer

0

Step-by-step solution

Let, S = 20 19 + 2 21 20 18 + 3 21 2 20 17 + . . . + 20 21 19 ⇒ S = 20 19 + 2 · 20 19 · 21 20 + 3 20 19 21 20 2 + . . . + 20 20 19 · 21 20 19 ⇒ S = 20 19 1 + 2 · 21 20 + 3 21 20 2 + . . . + 20 21 20 19 Now on comparing with S = k · 20 19 we get, ⇒   k = 1 + 2 · 21 20 + 3 21 20 2 + . . . . + 20 21 20 19   . . . . 1 ⇒ 21 20 k = 21 20 + 2 21 20 2 + . . . + 19 21 20 19 + 20 21 20 20     . . . . 2 Now on subtracting above equations we get, ⇒

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