Evaluate the following series :

(i) 1 + 2 + 3 +............+ 60 Solution

(ii) 3 + 6 + 9 + ............+ 96 Solution

(iii) 51 + 52 + 53 +............+ 92 Solution

(iv) 1 + 4 + 9 + 16 +...............+ 225 Solution

(v) 6^{2} + 7^{2} + 8^{2} +........+21^{2} Solution

(vi) 10^{3} + 11^{3} + 12^{3} +.........+ 20^{3} Solution

(vii) 1 + 3 + 5 +.............+ 71 Solution

(2) If 1 + 2 + 3 + ...........+ k = 325 , then find 1^{3} +2^{3} + 3^{3} +......+ k^{3}. Solution

(3) If 1^{3} + 2^{3} + 3^{3} +............+ k^{3} = 44100 then find 1 + 2 + 3 +......+k . Solution

(4) How many terms of the series 1^{3} + 2^{3} + 3^{3} +............ should be taken to get the sum 14400? Solution

(5) The sum of the squares of the first n natural numbers is 285, while the sum of their cubes is 2025. Find the value of n. Solution

(6) Rekha has 15 square colour papers of sizes 10 cm, 11 cm, 12 cm,…, 24 cm. How much area can be decorated with these colour papers? Solution

(7) Find the sum of the series (2^{3} - 1) + (4^{3} - 3^{3}) + (6^{3} - 5^{3})+....... to (i) n terms (ii) 8 terms Solution

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