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Find the sum of the series whose nth term is given by:

(3n^{2} + 2n)

n (n + 1) (n + 4)

(4n^{3} + 6n^{2} + 2n)

(3n^{2} – 3n + 2)

(2n^{2} – 3n + 5)

(n^{3} – 3^{n})

Find the sum of the series:

(2^{2} + 4^{2} + 6^{2} + 8^{2} + … to n terms)

(2^{3} + 4^{3} + 6^{3} + 8^{3} + … to n terms)

(5^{2} + 6^{2} + 7^{2} + … + 20^{2})

(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + … to n terms

(3 × 8) + (6 × 11) + (9 × 14) + … to n terms

(1 × 2^{2}) + (2 × 3^{2}) + (3 × 4^{2}) + … to n terms

(1 × 2^{2}) + (3 × 3^{2}) + (5 × 4^{2}) + … to n terms

(3 × 1^{2}) + (5 × 2^{2}) + (7 × 3^{2}) + … to n terms

(1 × 2 × 3) + (2 × 3 × 4) + (3 × 4 × 5) + … to n terms

(1 × 2 × 4) + (2 × 3 × 7) + (3 × 4 × 10) + … to n terms

…. To n terms

to n terms

3 + 15 + 35 + 63 +...to n terms

1 + 5 + 12 + 22 + 35 +... to n terms

5 + 7 + 13 + 31 + 85 + …. To n terms

If, prove that,

.

If S_{n} denotes the sum of the cubes of the first n natural numbers and s_{n} denotes the sum of the first n natural numbers then find the value of .

Find the sum (2 + 4 + 6 + 8 +… + 100).

Find the sum (41 + 42 + 43 + …. + 100).

Find the sum 11^{2} + 12^{2} + 13^{2}+ …20^{2}

Find the sum 6^{3} + 7^{3} + 8^{3} + 9^{3} + 10^{3}.

If , find the value of .

If, find the value of.

Find the sum of the series {2^{2} + 4^{2} + 6^{2} + …. + (2n)^{2}}

Find the sum of 10 terms of the geometric series

Find the sum of n terms of the series whose r^{th} term is (r + 2^{r}).