Let a - n - n -2- n - n - 2- n -1- bn - a - n -1- a - n - 11-Cn -b-n-1-b- n- d- n-C-n-1-C- n d o t s andSo on z n - y n -1- y n - n - NThe value of n for which xn- yn- Zn are in G-P isA- 5B- 7C- 9D- no value of n exists

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Law of Reciprocal

Let a - n = n...

Question

Let $a_{n} = n {.2}^{n} + n^{2} + n + 1, b n = a_{n + 1} - a_{n}, C_{n} = b_{n + 1} - b_{n}, d_{n} = C_{n + 1} - C_{n} \dots$ and
So on $z_{n} = y_{n + 1} - y_{n} \forall n ϵ N$

The value of n for which $x_{n}, y_{n}, z_{n}$ are in G.P is

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no value of n exists

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a_{n} = n {.2}^{n} + n^{2} + n + 1, b n = a_{n + 1} - a_{n}, C_{n} = b_{n + 1} - b_{n}, d_{n} = C_{n + 1} - C_{n} \dots

Z_{n} = y_{n + 1} - y_{n} \forall n ϵ N

y_{2} + z_{2}, y_{3} + z_{3}, y_{4} + z_{4}

a = \sum_{n = 0}^{\infty} x^{n}, b = \sum_{n = 0}^{\infty} y^{n}, c = \sum_{n = 0}^{\infty} (x y)^{n}

| x |, | y | < 1

x (n) = {(\frac{1}{3})}^{n} u (n), w h e r e u (n) = {\begin{matrix} 1, & n \geq 0 0, & n < 0 \end{matrix}

y (n) = x (- n), - \infty < n < \infty

\infty \sum n = - \infty y (n)

Find the value of $^{n} C_{0} . (n + 1) + n .^{n} C_{1} + (n - 1)^{n} C_{2} . . . . 1.^{n} C_{n}$

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{n} & x^{n + 2} & x^{n + 3} y^{n} & y^{n + 2} & y^{n + 3} z^{n} & z^{n + 2} & z^{n + 3} \end{matrix} ∣ ∣ ∣ ∣ ∣

= (x - y) (y - z) (z - x) (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})

n

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