# How to solve i+i^2+i^3+i^4 upto 101 terms

Welcome to my article How to solve i+i^2+i^3+i^4 upto 101 terms. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question How to solve i+i^2+i^3+i^4 upto 101 terms, read and understand it carefully till the end.

Let us know how to solve this question How to solve i+i^2+i^3+i^4 upto 101 terms.

First write the question on the page of the notebook.

## How to solve i+i^2+i^3+i^4 upto 101 terms

First write this question as follows and then solve,

\displaystyle i+{{i}^{2}}+{{i}^{3}}+{{i}^{4}}……………101terms

here,

a = i

n = 9

r = \displaystyle \frac{{{{i}^{2}}}}{i} = i

Formula

\displaystyle {{S}_{n}}=\frac{{a({{r}^{n}}-1)}}{{r-1}}

Substituting the values of a , r , n in this formula,

\displaystyle {{S}_{n}}=\frac{{i({{i}^{{101}}}-1)}}{{i-1}}

\displaystyle {{S}_{n}}=\frac{{i({{i}^{{100}}}\times {{i}^{1}}-1)}}{{i-1}}

we know that ,

\displaystyle i=i

\displaystyle {{i}^{2}}=-1

\displaystyle {{i}^{3}}=-i

\displaystyle {{i}^{4}}=1

so,

\displaystyle {{S}_{n}}=\frac{{i\left[ {{{{{{{{(i)}}^{4}}}}}^{{25}}}\times {{i}^{1}}-1)} \right]}}{{i-1}}

\displaystyle {{S}_{n}}=\frac{{i\left[ {{{1}^{{25}}}\times i-1)} \right]}}{{i-1}}

\displaystyle {{S}_{n}}=\frac{{i\left[ {1\times i-1)} \right]}}{{i-1}}

\displaystyle {{S}_{n}}=\frac{{i\left[ {i-1)} \right]}}{{i-1}}

\displaystyle {{S}_{n}}=i

i+i^2+i^3+i^4 upto 101 terms = i [Answer]

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