S = 1 × 6 + 2 × 7 + 3 × 8 + . . . . . . . . . . . . . . . + 15 × 20 , what is the value of S? Options: A . &nbsp 1841 B . &nbsp 1840 C . &nbsp 2871 D . &nbsp 2870

Answer: Option B : B T n = n ( n + 5 ) = n 2 + 5 n S n = ∑ T n = ∑ n 2 + 5 ∑ n = n ( n + 1 ) ( 2 n + 1 ) 6 + 5 × n ( n + 1 ) 2 ; Put n = 15 S n = 1840

S=1×6+2×7+3×8+...............+15×20, what is the value of

Question

$S = 1 \times 6 + 2 \times 7 + 3 \times 8 + . . . . . . . . . . . . . . . + 15 \times 20$ , what is the value of S?

Options:

A . 1841

B . 1840

C . 2871

D . 2870

Answer: Option B
:
B

$T_{n} = n (n + 5) = n^{2} + 5 n$

$S_{n} = \sum T_{n} = \sum n^{2} + 5 \sum n$

$= \frac{n (n + 1) (2 n + 1)}{6} + 5 \times \frac{n (n + 1)}{2}$ ; Put n = 15

$S_{n}$ = 1840

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