1- - a- a2- - a3- -n terms if a - 1-

[ r= a / 1 = a; In =A r^ n 1 ( a=first term ) #160;; =1.( a ) ^ n 1 ...

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Geometric Progression

1, - a, a2, -...

Question

$1, - a, a^{2}, - a^{3}, . . . . n$ terms $(i f a \neq - 1) .$

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Solution

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1, - a, a^{2}, - a^{3}, . . . n

a \neq - 1

a_{1}, a_{2}, a_{3}, . . ., a_{n}

\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \frac{1}{a_{3} a_{4}} + . . . \frac{1}{a_{n - 1} a_{n}} = \frac{n - 1}{a_{1} a_{n}}

1 + (1 + a) + (1 + a + a^{2}) + (1 + a + a^{2} + a^{3}) + . . . .

a, a_{2}, a_{3}, . . . ., a_{n}

n

a = 0

d \neq 0

\frac{a_{3} - a_{2}}{a_{2}} + \frac{a_{4} - a_{2}}{a_{3}} + \frac{a_{5} - a_{2}}{a_{4}} . . . . + \frac{a_{n} - a_{2}}{a_{n - 1}}

n

1, - a, a^{2}, - a^{3} . . . .

a \neq - 1

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