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COMEDK2015MathematicsSequences and Series

11³+12³+13³+ . .+20³ is

Options

  1. Aan even integer.
  2. Ban odd integer divisible by 5 .
  3. Cmultiple of 10 .
  4. Dan odd integer but not a multiple of 5 .

Correct answer

B. an odd integer divisible by 5 .

Step-by-step solution

We have, aligned 11³+12³+13³+ +20³ = (1³+2³+ +10³+11³+ .& .12³+ .+20³ ) &- (1³+2³+ .+10³ ) aligned aligned &= (20)³- (10)³ &= ( 20(20+1) 2 )²- ( 10(10+1) 2 )² &=(10 21)²-(5 11)²=(210-55)(210+55) &=155 265=41075=5 8215 aligned

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