Question

Find the 12th partial sum of ∞∑  (-2i-10)i-1

Answer 1

Answer:

The 12th partial sum of the given series is:

                                -276

Step-by-step explanation:

We are asked to find the 12th partial sum of the series which is given by:

             $\sum_{i=1}^{\infty}(-2i-10)$

i.e. we have to find the sum of first 12 terms.

i.e.

$\sum_{i=1}^{12}(-2i-10)$

which could also be simplified by the method:

$\sum_{i=1}^{12}(-2i-10)=-2\sum_{i=1}^{12}i-10\sum_{i=1}^{12}1$

which is further given by:

$\sum_{i=1}^{12}(-2i-10)=-2\times (1+2+3+4+5+6+7+8+9+10+11+12)-10\times (1+1+1+1+1+1+1+1+1+1+1+1)$

know we know that:

$1+2+3+.....+n=\dfrac{n(n+1)}{2}$

i.e.

$1+2+3+....+12=\dfrac{12\times 13}{2}\\\\1+2+3+....+12=78$

Hence, we get:

$\sum_{i=1}^{12}(-2i-10)=-2\times 78-10\times 12\\\\[tex]\sum_{i=1}^{12}(-2i-10)=-156-120\\\\[tex]\sum_{i=1}^{12}(-2i-10)=-276$

           Hence, the answer is:  -276

Answer 2

Hello,


$\sum_{i=1}^{12}(-2i-10)=-10\sum_{i=1}^{12}1-2\sum_{i=1}^{12}i$

$=-120-2*13*12/2=-120-156=-276$