3
Question
Let xn=(1−13)2(1−16)2(1−110)2........⎛⎜
⎜
⎜⎝1−1n(n+1)2⎞⎟
⎟
⎟⎠2,n≥2.
Then the value of limn→∞xn is
Let xn=(1−13)2(1−16)2(1−110)2........⎛⎜
⎜
⎜⎝1−1n(n+1)2⎞⎟
⎟
⎟⎠2,n≥2.
Then the value of limn→∞xn is
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Solution
The correct option is B 1/9
xnxn−1=(1−2n(n+1))2=(n+2n)2(n+1n−1)2
so comparing xn=A.(n+2n)2, A is real constant,
now, x2=49. So A=19.
so limn→∞xn=A=19
xnxn−1=(1−2n(n+1))2=(n+2n)2(n+1n−1)2
so comparing xn=A.(n+2n)2, A is real constant,
now, x2=49. So A=19.
so limn→∞xn=A=19
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