(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + ...... + x^{100}) when written in as

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7.Binomial Theorem

normal

$(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + ...... + x^{100})$ when written in the ascending power of $x$ then the highest exponent of $x$ is ______ .

A

$4950$

B

$5050$

C

$5150$

D

none

Solution

Highest exponent in the product of first two is $3 = 1 + 2$

Highest exponent in the product of first three is $6 = 1 + 2 + 3$

Similarly, Highest exponent in the product of first hundred

$= 1 + 2 + …… + 100 = 5050$

Standard 11

Mathematics

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