very easy

Algebra Level 4

Find the value of coefficient of x 99 x^{99} (x raise to the power 99) in the below given expansion :-

( x + 1 ) ( x + 3 ) ( x + 5 ) . . . . . . ( x + 199 ) (x+1)(x+3)(x+5)......(x+199)


The answer is 10000.

Samanvay Vajpayee by Samanvay Vajpayee , 21, Canada

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3 solutions

Santanu Banerjee
Jan 9, 2015

1+3+5+...+197+199

∑ n = 1 100 \sum_{n=1}^{100} (2n-1) = 10000

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Aareyan Manzoor
Jan 16, 2015

lets see vieta's. ( x + n 1 ) ( x + n 2 ) ( x + n 3 ) ( x + n 4 ) ⋯ ⋯ ( x + n i ) = x i + ∑ i = 1 i n i x i − 1 + . . . . . . . . (x+n_1)(x+n_2)(x+n_3)(x+n_4)\dotsm\dotsm (x+n_i)=x^i +\sum_{i=1}^i n_i x^{i-1}+_........ from this we can say that that the coefficient of x 99 \quad x^{99}\quad is 1 + 3 + 5 + ⋯ ⋯ 199 = 10 0 2 = 10000 1+3+5+\dotsm\dotsm 199=100^2=\boxed{10000}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Abu Zubair
Jan 10, 2015

thye following was asked in FTRE 2014

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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