The sum of the co-efficients in the expansion of (1+5x-7x^3) ^2020
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2 thoughts on “The sum of the co-efficients in the expansion of (1+5x-7x^3) ^2020<br />of​”

1. Given : (1+5x-7x³)²⁰²⁰

   To Find : sum of the co-efficients in the expansion

   Solution:

   P(x) = (1+5x-7x³)²⁰²⁰

   => P(x) = 1 + coefficient and terms with power of x

   if we put x = 1

   => P(1) + 1 + sum of other coefficient

   => P(1) = sum of other coefficient

   P(1) = (1+5-7)²⁰²⁰ = (-1)²⁰²⁰

   = ((-1)²)¹⁰¹⁰

   = 1¹⁰¹⁰

   = 1

   The sum of the co-efficients in the expansion of (1+5x-7x^3) ^2020 is 1

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2. Step-by-step explanation:

   Given:

   [tex]( {1 + 5x – 7 {x}^{3} )}^{2020} \\ [/tex]

   To find: Sum of coefficients in the given expansion

   Solution:

   To find Sum of coefficients in the given expansion put x=1

   [tex]( {1 + 5(1) – 7( {1}^{3})) }^{2020} \\ \\ [/tex]

   Now,solve

   [tex] = > ( {1 + 5 – 7)}^{2020} \\ \\ = > {(6 – 7)}^{2020} \\ \\ = > {( – 1)}^{2020} \\ \\ = > 1 \\ \\ [/tex]

   Because 2020 is even number.

   we know that when power is even and base is negative,then result is positive.

   Final Answer:Sum of coefficients in the expansion of

   [tex]\bold{( {1 + 5x – 7 {x}^{3} )}^{2020}} \\ [/tex]

   is 1.

   Hope it helps you.

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