Question

Rewrite the following in $\sum$ notation: (a) $x_{1}\left(x_{1}-1\right)+2 x_{2}\left(x_{2}-1\right)+3 x_{3}\left(x_{3}-1\right)$ (b) $a_{2}\left(x_{3}+2\right)+a_{3}\left(x_{4}+3\right)+a_{4}\left(x_{5}+4\right)$ (c) $\frac{1}{x}+\frac{1}{x^{2}}+\dots+\frac{1}{x^{n}} \quad(x \neq 0)$ (d) $1+\frac{1}{x}+\frac{1}{x^{2}}+\cdots-\frac{1}{x^{n}} \quad(x \neq 0)$

          Rewrite the following in $\sum$ notation:
(a) $x_{1}\left(x_{1}-1\right)+2 x_{2}\left(x_{2}-1\right)+3 x_{3}\left(x_{3}-1\right)$
(b) $a_{2}\left(x_{3}+2\right)+a_{3}\left(x_{4}+3\right)+a_{4}\left(x_{5}+4\right)$
(c) $\frac{1}{x}+\frac{1}{x^{2}}+\dots+\frac{1}{x^{n}} \quad(x \neq 0)$
(d) $1+\frac{1}{x}+\frac{1}{x^{2}}+\cdots-\frac{1}{x^{n}} \quad(x \neq 0)$

Added by Rachel P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/24/2023

Step 1

We can rewrite this as a sum from $i=1$ to $3$: $$\sum_{i=1}^{3} i x_i (x_i - 1)$$ Show more…

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Rewrite the following in $\sum$ notation: (a) $x_{1}\left(x_{1}-1\right)+2 x_{2}\left(x_{2}-1\right)+3 x_{3}\left(x_{3}-1\right)$ (b) $a_{2}\left(x_{3}+2\right)+a_{3}\left(x_{4}+3\right)+a_{4}\left(x_{5}+4\right)$ (c) $\frac{1}{x}+\frac{1}{x^{2}}+\dots+\frac{1}{x^{n}} \quad(x \neq 0)$ (d) $1+\frac{1}{x}+\frac{1}{x^{2}}+\cdots-\frac{1}{x^{n}} \quad(x \neq 0)$