Solve - 3-6 - 6-9 - 9-12 - - - 3 n 3 n - 3 - 3 n n - 1 n - 2

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Sum of n Terms

Solve : 3.6...

Question

Solve : $3.6 + 6.9 + 9.12 + \dots + 3 n (3 n + 3) = 3 n (n + 1) (n + 2)$

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Solution

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Similar questions

3.6 + 6.9 + 9.12 + . . . + 3 n (3 n + 3) =

1 + \frac{2 n}{3} + \frac{2 n (2 n + 2)}{3.6} + \frac{2 n (2 n + 2) (2 n + 4)}{3.6.9} + . . . . .

= 2^{n} {1 + \frac{n}{3} + \frac{n (n + 1)}{3.6} + \frac{n (n + 1) (n + 2)}{3.6.9} + . . . .}

\frac{1}{1.2.3} + \frac{1}{2.3.4} + \frac{1}{3.4.5} + \dots + \frac{1}{n (n + 1) (n + 2)} = \frac{n (n + 3)}{4 (n + 1) (n + 2)}

Question 1(n) :

Solve:

$\frac{4}{3} - \frac{1}{2}$

n

\frac{1}{(n - 1) (n - 2)} + \frac{1}{(n - 2) (n - 3)} = \frac{2}{3}, n \neq 1, 2, 3,

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