Question

14²+15²+...........30²=?

Answer 1

Answer: 8636

Step-by-step explanation:

When we subtract the sum of squares of first 13 natural numbers from the sum of squares of first 30 natural numbers, we get the answer.

14² + 15² +......+ 30² = (1² + 2² +......+ 30²) - (1² + 2² +......+ 13²)

Sum of squares of first n natural numbers is [n(n + 1)(2n + 1)]/6.

S_n = [n(n + 1)(2n + 1)] / 6

S_30 = [30(30 + 1)(2 × 30 + 1)] / 6

S_30 = [30 × 31 × 61] / 6

S_30 = 56730 / 6

S_30 = 9455

S_13 = [13(13 + 1)(2 × 13 + 1)] / 6

S_13 = [13 × 14 × 27] / 6

S_13 = 4914 / 6

S_13 = 819

∴ Answer = 9455 - 819 = 8636

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Answer 2

Answer:

Step-by-step explanation:

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