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10^2+12^2+14^2+......+26^2=??

10^2+12^2+14^2+......+26^2=??
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3 votes
10^2+12^2+14^2+......+26^2=??

User Dudeldidadum
by
8.2k points

1 Answer

6 votes

Answer:

3156

Explanation:

  • Used formula:
  • (1² + 2² + 3² + ... + n²) =1/6*n(n + 1)(2n + 1)

--------

  • 10²+12²+14²+......+26² =
  • (2*5)²+(2*6)² + (2*7)² + ... + (2*13)² =
  • 4*(5²+6²+7²+...+13²) =
  • 4*(1²+2²+...+13² - (1²+2²+3²+4²)) =
  • 4*(1/6*13(13+1)(2*13+1) - (1+4+9+16)) =
  • 4*(1/6*13*14*27- 30) =
  • 4*(819 - 30) =
  • 4*789 =
  • 3156
User Vincentvanjoe
by
8.4k points
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