Question

2015
1
Evaluate Σ
¡4m+k
meN .
k=1​

Answer 1

To find the simplification of question:

Answer 2

Given:

k = 1

To Find:

i

Solution:

∑ $\frac{1}{i^{4m4k} }$

= ∑ $\frac{1}{i^{4m}i^{k} }$

= ∑ $\frac{1}{i^{m} }$ × $\frac{i^{3k} }{i^{3k} }$ = ∑$\frac{i^{3k} }{i^{4k} }$

= ∑$i^{3k}$

Then,

⇒ 2015∑k=1 = i³ + $i^{6}$ +..2015term

⇒ $\frac{i^{3}[(i^{3})^{2015}-1 ) }{i^{3}-1 }$

⇒$\frac{i^{3}[(-1)^{5}-1 }{-i-1}$

⇒ $i^{3}$ = -i