Question

1. The degree of this polynomial 2-y-y a),
52,
2. The coefficient of xin 1/2 x+3x is a)1,
b)2. c)3. d) 1/2 63
ca. d)s​

Answer 1

Answer:

ANSWER

(1+x)(1+2x)(1+3x)......(1+100x)

We are required to find the coefficient of

′

x

′

in the above expansion.

Now, first multiply the first two terms

(1+x)(1+2x)=1+x+2x+2x

2

=1+(1+2)x+2x

2

Similarly multiply the first three terms

(1+x)(1+2x)(1+3x)=1+(1+2+3)x+11x

2

+6x

3

So in the expansion of (1+x)(1+2x)(1+3x)......(1+100x)

coefficient of x should be (1+2+3+........+100)

We know that the sum of the first

′

n

′

natural numbers is given by the expression

2

n(n+1)

∴ Coefficient of x in the above expansion is =

2

100×101

=5050.

Explanation:

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