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Differential Calculus> =5 +n/1 + n(n-1) / 2! + ….....+ n!/n! nex...

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=5 +n/1 + n(n-1) / 2! + ….....+ n!/n!
next step I want to understand
(1+1)^n + 4 = 2^n + 4

milind , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Hello student,
Please find answer to your question
$L = 5 + n + \frac{n(n-1)}{2!} +.............+ \frac{n!}{n!}$
$L = 4+1 + n + \frac{n(n-1)}{2!} +.............+ \frac{n!}{n!}$
$L = 4+(1 + n + \frac{n(n-1)}{2!} +.............+ \frac{n!}{n!})$
Using binomial theorm,
$(1+x)^{n} = \frac{n!}{n!}1^{n}x^{0} + \frac{n!}{(n-1)!}1^{n-1}x + \frac{n!}{2!(n-2)!}1^{n-1}x^{2} +.............+ \frac{n!}{n!}1^{0}x^{n}$ By comparison, we have
x = 1
$L = 4 + (1+1)^{n}$
$L = (2)^{n} + 4$

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