Question

solve the series: 6^2+7^2+8^2+.....+50^2

Answer 1

6^2+7^2+8^2+............+50^2
= 36+49+64+............+2500
= Sn = n/2(a+l)
= Sn = 45/2(36+2500)
= Sn = 45×1268
= Sn = 17060
Therefore, 6^2+7^2+8^2+........+50^2 = 17060.

Answer 2

6^2+7^2+......+50^2
=(1^2+2^2+.....+50^2)-(1^2+2^2+....+5^2)
=n(n+1)(2n+1)/6 - n(n+1)(2n+1)/6
=50×51×101/6 - 5×6×11/6
=257550/6 - 330/6
=257550-330 / 6
=257220/6
=42870