Respuesta :

mhanifa

Answer:

  • See below

Step-by-step explanation:

Find the sum:

  • 1/2n(n+1) + 1/2(n+1)(n+2) =
  • 1/2(n² + n) + 1/2(n² + 3n + 2) =
  • 1/2(n² + n + n² + 3n + 2) =
  • 1/2(2n² + 4n + 2) =
  • n² + 2n + 1 =
  • (n + 1)²

Proved

Solution:

Work:

  • [1/2(n)(n + 1)] + [1/2(n + 1)(n + 2)]

Simplifying in Brackets

  • => [1/2(n² + n)] + [1/2(n² + 2n + n + 2)]
  • => [n²/2 + n/2] + [n²/2 + n + n/2 + 1]

Removing Brackets.

  • => n²/2 + n/2 + n²/2 + n + n/2 + 1

Solving.

  • => n² + n + 1
  • => (n + 1)²

Since the result has a "square" sign, the statement is proved has true.

Hoped this helped.

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