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Sum of Infinite Terms of a GP

If Sn denot...

Question

If $S_{n}$ denote the sum of $n$ terms of a geometric progression, whose first term is a, and common ratio $r$ , then the sum of $S_{1}, S_{3}, S_{5},, S_{2 n - 1}$ can be

A

\frac{a}{r - 1} {\frac{r^{2} (r^{2 n} - 1)}{r^{2} - 1} - n}

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B

\frac{a r}{r - 1} {\frac{r (r^{2 n} - 1)}{r^{2} - 1} - n}

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C

\frac{a}{r - 1} {\frac{r (r^{2 n} - 1)}{r^{2} - 1} - n}

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D

N o n e o f t h e s e

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Solution

The correct option is D $N o n e o f t h e s e$

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Similar questions

S_{n}

denote the sum of

n

terms of a G.P. whose first term is

a

, a n d c o m m o n r a t i o

, f i n d t h e s u m o f

S_{1}, S_{3}, S_{5}, ...S_{2n - 1}$.

S_{n}

represents the sum of

n

G . P .

whose first term and common ratio are

a

r

respectively, then prove that

S_{1} + S_{2} + S_{3} + . . . + S_{n} = \frac{n a}{1 - r} - \frac{a r (1 - r^{n})}{{(1 - r)}^{2}}

S_{n}

represents the sum of

n

G . P .

whose first term and common ratio are

a

r

respectively, then prove that

S_{1} + S_{3} + S_{5} + . . . + S_{2 n - 1} = \frac{a n}{1 - r} - \frac{a r (1 - r^{2 n})}{{(1 - r)}^{2} (1 + r)}

S_{1}, S_{2}, S_{3} \dots \dots, S_{n}, \dots

are the sums of infinite geometric series whose first terms are

1, 2, 3, \dots \dots n, \dots \dots

and whose common ratios are

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots \dots \frac{1}{n + 1} \dots \dots

respectively, then the value of

2 n - 1 \sum r = 1 S_{r}^{2}

2 n

terms of a geometric progression whose first term is

^{'} a^{'}

and common ratio

^{'} r^{'}

is equal to the sum of

n

terms of a geometric progression whose first term is

^{'} b^{'}

r^{2}

b

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Sum of Infinite Terms of a GP

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