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Nomenclature of Carboxylic Acid Derivatives

What is formu...

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What is formula for product of GP upto infinite and n terms?

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Q. In a GP the product of the first four terms is

4

and the second term is the reciprocal of the fourth term. The sum of the GP up to infinite terms is

P_{n}

is the sum of a

G P

n

terms. Show that

(1 - r) \frac{d p_{n}}{d r} = n . P_{n - 1} - (n - 1) P_{n}

Q. The sum of first two terms of a GP is

\frac{14}{5}

and the sum of infinite terms is

\frac{10}{3}

. The first term of the GP if the common ratio is positive is___.

Sum to infinite terms of the GP $\frac{2}{5}, \frac{3}{5^{2}}, \frac{2}{5^{3}}, \frac{3}{5^{4}} . .$ is ___.

Q. In a GP of n terms, if n is odd then the product of all terms =

M^{n}

, where M is the middle term.

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