The value of the sum n=1∑13(in+in+1), where i=−1, equals

Note ik+ik+1+ik+2+ik+3=0 .Hence ∑n=113in=i13=i and ∑n=113in+1=i14=−1.Thus the given sum is i−1.

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The value of the sum _{n=1}^{13} (i^n + i^{n+1}), where i = {

Question

The value of the sum $n = 1 \sum 13 (i^{n} + i^{n + 1})$ , where $i = - 1$ , equals

i

i - 1

- i

0

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Scarlett Discussed

The value of the sum

n = 1 \sum 13 (i^{n} + i^{n + 1})

, where

i = - 1

, equals

9 mins ago

Discuss this question LIVE

9 mins ago

Note

i^{k} + i^{k + 1} + i^{k + 2} + i^{k + 3} = 0

Hence

\sum_{n = 1}^{13} i^{n} = i^{13} = i

and

\sum_{n = 1}^{13} i^{n + 1} = i^{14} = - 1

Thus the given sum is

i - 1

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Question Text	The value of the sum $n = 1 \sum 13 (i^{n} + i^{n + 1})$ , where $i = - 1$ , equals
Answer Type	Text solution:1
Upvotes	150