1.

Find the value of (13 – 12 + 23 – 22 + 33 – 32 + ….. + 103 – 102).1). 22802). 24603). 26404). 2820

Answer»

As we KNOW,

⇒ Sum of first ‘N’ terms of square series = (12 + 22 + … + n2) = n(n + 1)(2n + 1)/6

⇒ Sum of first ‘n’ terms of CUBE series = (13 + 23 + … + n3) = [n(n + 1)/2]2

We can write,

⇒ (13 – 12 + 23 – 22 + 33 – 32 + ….. + 103 – 102) = (13 + 23 + 33 + ….. + 103) – (12 + 22 + 32 + ….. + 102) = {(10 × 11)/2}2 – {(10 × 11 × 21)/6} = 3025 – 385 = 2640


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