Coefficient of x 48 in ∑ r = 0 50 C 50 r x - 2 r 3 50 - r, C 50 2, C 48 2, 3 48, 2 48

∑ r = 0 50 C 50 r 3 50 - r x - 2 r = 3 + x - 2 50 = x + 1 50 Coefficient of x 48 in 1 + x 50 is C 50 48 = C 50 2

Coefficient of x 48 in ∑ r = 0 50 C 50 r x - 2 r 3 50

Question: Answered & Verified by Expert

Coefficient of

x^{48}

\sum_{r = 0}^{50} ({{}^{50}C}_{r}) {(x - 2)}^{r} 3^{50 - r}

MathematicsBinomial TheoremJEE Main

Options:

Solution:

1867 Upvotes Verified Answer

The correct answer is:

{{}^{50}C}_{2}

\sum_{r = 0}^{50} ({{}^{50}C}_{r}) (3^{50 - r}) {(x - 2)}^{r}

= {(3 + (x - 2))}^{50}

= {(x + 1)}^{50}

Coefficient of

x^{48}

{(1 + x)}^{50}

{{}^{50}C}_{48} = {{}^{50}C}_{2}

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