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Question: If A<sub>n</sub> is the area bounded by y = x and y = x<sup>n</sup>, nÎ N, then A<sub>2</sub> . A<s...

If An is the area bounded by y = x and y = xn, nÎ N, then

A2 . A3 ........ An =

A

1n(n+1)\frac { 1 } { n ( n + 1 ) }

B

12nn(n+1)\frac { 1 } { 2 ^ { \mathrm { n } } \mathrm { n } ( \mathrm { n } + 1 ) }

C
D
Answer
Explanation

Solution

An = =

= =

Thus A2 . A3 . A4 ..... An = 12n−1(13⋅24⋅35⋯n−1n+1)\frac { 1 } { 2 ^ { \mathrm { n } - 1 } } \left( \frac { 1 } { 3 } \cdot \frac { 2 } { 4 } \cdot \frac { 3 } { 5 } \cdots \frac { \mathrm { n } - 1 } { \mathrm { n } + 1 } \right)

=