Write the sum using sigma notation.
\[
1-2 x+3 x^{2}-4 x^{3}+5 x^{4}+\ldots-94 x^{93}
\]

Answer

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Answer

This is the sigma notation for the given series.

Steps

Step 1 ：First, we observe the pattern in the given series. We see that the coefficient of each term is one more than the power of \(x\) in the previous term.

Step 2 ：The power of \(x\) in each term is one less than the coefficient of the term.

Step 3 ：The sign of each term alternates, starting with positive.

Step 4 ：We can express this pattern using sigma notation as follows:

Step 5 ：\(\sum_{n=0}^{93} (-1)^n (n+1) x^n\)

Step 6 ：This is the sigma notation for the given series.

Write the sum using sigma notation.\[1-2 x+3 x^{2}-4 x^{3}+5 x^{4}+\ldots-94 x^{93}\]

Answer

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Write the sum using sigma notation.
\[
1-2 x+3 x^{2}-4 x^{3}+5 x^{4}+\ldots-94 x^{93}
\]