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Question: The \(n ^ { t h }\) term of the following series \(( 1 \times 3 ) + ( 3 \times 5 ) + ( 5 \times 7 ...

The nthn ^ { t h } term of the following series

(1×3)+(3×5)+(5×7)+(7×9)+……( 1 \times 3 ) + ( 3 \times 5 ) + ( 5 \times 7 ) + ( 7 \times 9 ) + \ldots \ldots will be.

A

n(2n+1)n ( 2 n + 1 )

B

2n(2n−1)2 n ( 2 n - 1 )

C

(2n+1)(2n−1)( 2 n + 1 ) ( 2 n - 1 )

D

4n2+14 n ^ { 2 } + 1

Answer

(2n+1)(2n−1)( 2 n + 1 ) ( 2 n - 1 )

Explanation

Solution

Since, given series

Hence nthn ^ { t h } term of the series is (2n+1)(2n−1)( 2 n + 1 ) ( 2 n - 1 ).