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Question

The sum of the nth term of the series 1.2.5 + 2.3.6 + 3.4.7 + .....n terms is 112n(n+1)(3n2+23n+34)

A
True
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B
False
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Solution

The correct option is A True
We have,
1.2.5+2.3.6+3.4.7+.......+n terms

1(1+1)(1+4)+2(2+1)(2+4)+3(3+1)(3+4)+............+n terms

Therefore, the general term
n(n+1)(n+4)

Now, the sum of this series will be
nk=1k(k+1)(k+4)
nk=1(k3+5k2+4k)

Therefore,
(n(n+1))24+5n(n+1)(2n+1)6+4n(n+1)2

n(n+1)2(n(n+1)2+5(2n+1)3+4)

n(n+1)2(3n2+23n+346)

n(n+1)12(3n2+23n+34)

Hence, this is the answer.

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