The sum of the series i-i2-i3- upto 1000 terms is

I + i2 + nbsp;i3 +_____ 1000 terms i.e i + i2 + nbsp;i3 + i4 _____ + i1000 = i + i2 ndash; i + 1 + i5 _____ + i1000 = i ndash; 1 ndash; i + 1 + i5 ...

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Standard XII

Mathematics

Sum of n Terms

The sum of th...

Question

The sum of the series i + i² + i³ +_ upto 1000 terms is ________.

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Solution

i + i² + i³ +___ 1000 terms
i.e i + i² + i³ + i⁴_ + i^1000

= i + i² – i + 1 + i⁵ _ + i¹⁰⁰⁰
= i – 1 – i + 1 + i⁵ + _ + i¹⁰⁰⁰
= 0 + i⁵ + i⁶ + + i¹⁰⁰
Similarly, sum of next form terms is also zero. (∵ 1000 = 4(250)
i.e multiple of 4
Hence, i + i² + i³ +_ i¹⁰⁰⁰ = 0

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The sum of the series i + i2 + i3 +_____ upto 1000 terms is ____________.

i + i2 + i3 +_____ 1000 terms i.e i + i2 + i3 + i4 _____ + i1000 = i + i2 – i + 1 + i5 _____ + i1000 = i – 1 – i + 1 + i5 + _______ + i1000 = 0 + i5 + i6 + ________ + i100 Similarly, sum of next form terms is also zero. (∵ 1000 = 4(250) i.e multiple of 4 Hence, i + i2 + i3 +_____ i1000 = 0

The sum of the series i + i² + i³ +_ upto 1000 terms is ________.