Sum the following series to n terms is -r - 1n rr -1 r - 2 r - 3

The correct option is B n(n + 1)(n + 2)(n + 3)(n + 4)/5 T_n = n(n + 1) (n + 2)(n + 3) =1/5[n(n + 1)(n + 2)(n + 3)((n + 4) (n 1))] = 1/5 ...

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Sum of n Terms

Sum the follo...

Question

Sum the following series to n terms is $\sum_{r = 1}^{n} r (r + 1) (r + 2) (r + 3)$

\frac{(n + 1) (n + 2) (n + 3) (n + 4)}{5}

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\frac{n (n + 1) (n + 2) (n + 3) (n + 4)}{5}

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\frac{n (n + 1) (n + 2) (n + 3) (n + 4) (n + 5)}{6}

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

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6

n - \frac{n (n - 1) (n - 2)}{⌊ 3} \cdot 3 + \frac{n (n - 1) (n - 2) (n - 3) (n - 4)}{⌊ 5} \cdot 3^{2} - . . . . .,

n - \frac{n (n - 1) (n - 2)}{⌊ 3} \cdot \frac{1}{3} + \frac{n (n - 1) (n - 2) (n - 3) (n - 4)}{⌊ 5} \cdot \frac{1}{3^{2}} - . . . . .,

1 \times n + 2 (n - 1) + 3 (n - 2) + \dots \dots + (n - 1) \times 2 + n \times 1

n

(1 \times 2 \times 3) + (2 \times 3 \times 4) + (3 \times 4 \times 5) + \dots

(1 + x)^{n} = n \sum r = 0^{n} C_{r} x^{n},

\frac{C_{0}}{1 \cdot 2} 2^{2} + \frac{C_{1}}{2 \cdot 3} 2^{3} + \frac{C_{2}}{3 \cdot 4} 2^{4} + \dots + \frac{C_{n}}{(n + 1) (n + 2)} 2^{n + 2}

n

n^{n + 1} - n {(n - 1)}^{n + 1} + \frac{n (n - 1)}{2!} {(n - 2)}^{n + 1} - \dots = \frac{1}{2} n (n + 1)!

n^{n} - (n + 1) {(n - 1)}^{n} + \frac{(n + 1) n}{2!} {(n - 2)}^{n} - \dots = 1

n

1^{n} - n 2^{n} + \frac{n (n - 1)}{1 \cdot 2} 3^{n} - \dots = {(- 1)}^{n} n!

{(n + p)}^{n} - n {(n + p - 1)}^{n} + \frac{n (n - 1)}{2!} {(n + p - 2)}^{n} - \dots = n!

n + 1

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