raushantiwari8294 raushantiwari8294

08-09-2020
Mathematics

contestada

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

Respuesta :

mhanifa mhanifa

18-09-2020

Answer:

3156

Step-by-step 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

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