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Question

1x+1+2x(x+1)(x+2)+3x2(x+1)(x+2)(x+3)+........(n terms)=?

A
1+xn(x+1)(x+2)(x+3)..(xn)
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B
1xn(x+1)(x+2)(x+3)..(x+n)
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C
1+xn(x1)(x2)(x3)..(xn)
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D
1xn(x+1)(x+2)(x+3)..(xn)
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Solution

The correct option is B 1xn(x+1)(x+2)(x+3)..(x+n)

Given

1x+1+2x(x+1)(x+2)+3x2(x+1)(x+2)(x+3)+........ (n terms)

=1xx+1+2x(x+1)(x+2)+3x2(x+1)(x+2)(x+3)+...... (n terms)

=1xx+1(12x+2)+3x2(x+1)(x+2)(x+3)+...... (n terms)

=1x2(x+1)(x+2)+3x2(x+1)(x+2)(x+3)+...... (n terms)

=1x2(x+1)(x+2)(13x+3)+...... (n terms)

=1x3(x+1)(x+2)(x+3)+...... (n terms)

Continuing in the same way, we get

1x+1+2x(x+1)(x+2)+3x2(x+1)(x+2)(x+3)+........(n terms)

=1xn(x+1)(x+2)(x+3)..(x+n)


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