Algebra> The coefficient of x⁻²⁶ in the expansion ...

The coefficient of x⁻²⁶ in the expansion of(x² - 2/x⁴)¹¹ is ??(prefer attached image if needed)

Sarvesh , 6 Years ago

Grade 12

1 Answers

Samyak Jain

Last Activity: 6 Years ago

To find : coefficient of x^–26 in expansion of (x² – 2/x⁴)¹¹.

General term in eapansion of (a + b)ⁿ is T_r+1 = ⁿC_r . a^{(n – r)}. b^r

Here general term is T_r+1 = ¹¹C_r . (x²)^{(11 – r)}. (– 2/x⁴)^r = ¹¹C_r . x²^{(11 – r)}. (– 2)^r / x⁴^r

i.e. T_r+1 = ¹¹C_r . x²^{2 – 2r}^{– 4r}. (– 2)^r = ¹¹C_r . x⁽²^{2 – 6r)}. (– 2)^r

For x^{– 26}, x⁽²^{2 – 6r)} = x^{– 26} i.e. 22 – 6r = – 26 $\Rightarrow$ 6r = 48

or r = 8. Now put r = 8 in T_r+1. We get

T₈₊₁ = ¹¹C₈ . x^{– 26}. (– 2)⁸ = (11 ! / 8 ! 3!) . 2⁸ x^{– 26} = (11.10.9 / 3.2) . 2⁸ x^{– 26}

T₉ = 165 . 2⁸ x^{– 26} = 330 . 2⁷ x^{– 26}

$\therefore$ required coefficient of x^{– 26} is 330 . 2⁷ .

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Algebra> The coefficient of x⁻²⁶ in the expansion ...

The coefficient of x⁻²⁶ in the expansion of(x² - 2/x⁴)¹¹ is ??(prefer attached image if needed)

Sarvesh , 6 Years ago

Samyak Jain

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

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