J's answer to Jollie's Secondary 4 E Maths Singapore question.
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Easy. You need to apply the formula twice.
Realise that 10² + 11² + 12² + ... 25² is the sum of squares from 10 to 25.
It is obtained by subtracting the sum of squares from 1 to 9 from the sum of squares from 1 to 25
= (1² + 2² + 3² + ... + 25²) - (1² + 2² + 3² + ... + 9²)
= 1/6 (25)(25 + 1)(2(25) + 1) - 1/6 (9)(9 + 1)(2(9) + 1)
= 1/6 (25)(26)(51) - 1/6 (9)(10)(19)
= 5525 - 285
= 5240
Realise that 10² + 11² + 12² + ... 25² is the sum of squares from 10 to 25.
It is obtained by subtracting the sum of squares from 1 to 9 from the sum of squares from 1 to 25
= (1² + 2² + 3² + ... + 25²) - (1² + 2² + 3² + ... + 9²)
= 1/6 (25)(25 + 1)(2(25) + 1) - 1/6 (9)(9 + 1)(2(9) + 1)
= 1/6 (25)(26)(51) - 1/6 (9)(10)(19)
= 5525 - 285
= 5240
Date Posted:
2 years ago
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