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AP EAMCET20227 Jul 2022Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The smallest integer n such that 1 45^ 46^ + 1 47^ 48^ + + 1 133^ 134^ = 1 (n^0 ) is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

aligned 1 45^ 46^ + 1 47^ 48^ + + 1 133^ 134^ aligned array r = 1 1^ [ (46^ -45^ ) 45^ 46^ + (48^ -47^ ) 47^ 48^ + + . . (134^ -133^ ) 133^ 134^ ] array array r = 1 1^ [ ( 45^ - 46^ )+ ( 47^ - 48^ ) . .+ + ( 133^ - 134^ ) ] array = 1 1^ 45^ = 1 1^ According to question, array rlrl & & 1 (n^ ) & = 1 1^ n & n & =1 array

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