Question

${1}^{2} + {2}^{2} + {3}^{2} +......... + {10}^{2}$
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Answer 1

EXPLANATION.

1²+2²+3²+4²+.......+ 10²

the sum of square of first n natural number,

⇒ ∑n² = 1² + 2² + 3² + 4² + .....+ n² = n ( n + 1)(2n + 1)/6.

Nth terms of an AP = 10.

put the value of N = 10 in formula we get,

⇒ 10(10 + 1)(2(10) + 1 )/6

⇒ 10(11)(21)/6

⇒ 385

1² + 2² + 3² + 4² +.....+10² = 385.

MORE INFORMATION.

(1) = sum of first N natural number,

⇒ ∑n = 1+2+3+4+.......+n = n(n + 1)/2.

(2) = sum of square of first N natural number,

⇒ ∑n² = 1²+2²+3²+4²+.....+n² = n(n + 1)(2n +1)/6.

(3) = sum of cube of first N natural number,

⇒ ∑n³ = 1³+2³+3³+4³+.....n³ = [ n(n+1)/2]²