Question

The sum series $i+2+3i+4+....$ upto $100$ terms where $i=\sqrt{-}1$ equals $p+iq$. Then p equals to

• A. 4
• B. 6
• C. 2550
• D. 20

Answer 1

The correct option is C 2550

$i+2+3i+4+5i+6+...100$ term

(i + 3i + 5i +...50 term) + (2 + 4 + 6 +...50 term)

$\Rightarrow i[1+3+5+...]+[2+4+6+...]$

$\Rightarrow i\times \frac{50}{2}[2\times 1+(50-1\left)2\right]+\frac{50}{2}[2\times 2+(50-1\left)2\right]$

$\{S_n=\frac{n}{2}[2a+(n-1)d\left]\right\}$

$\Rightarrow i\times 25\left[100\right]+25\left[102\right]$

$\Rightarrow 2500i+2550$

2550+2500i = P + iq

p = 2550, q = 2500