Question

find the value of n..
if n = 69^5 + 5×69^4 +10×69^3 + 10×69^2 + 5×59 + 1


Pls friends.. Help me with this questions❤️❤️❤️​

Answer 1

There's some error in the question.

In the question it is given as,

$n=69^5+5 \times 69^4+10 \times 69^3+10 \times 69^2+5 \times 59 + 1$

But it's actually,

$n=69^5+5 \times 69^4+10 \times 69^3+10 \times 69^2+5 \times \mathbf{69} + 1$

To find the value of 'n' in the question, we have to be familiar with the expansion of (a + b)⁵ !!!

$\Large (a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$

The value of 'n' in the question is in the form of this expansion.

Here 'a' is taken as 69 and 'b' is taken as 1.

We can also take 'a' and 'b' as 1 and 69 respectively.

$\begin{aligned}&n=69^5+5 \times 69^4+10 \times 69^3+10 \times 69^2+5 \times 69+1\\ \Longrightarrow\ \ &n=(69^5)+(5 \times 69^4\times 1^1)+(10 \times 69^3 \times 1^2)+(10 \times 69^2 \times 1^3)+(5 \times 69^1 \times 1^4)+(1^5)\\ \Longrightarrow\ \ &n=(69+1)^5 \\ \Longrightarrow\ \ &n=\mathbf{70^5} \\ \Longrightarrow\ \ &n=\mathbf{1680700000}\end{aligned}$

Hence the value of n is " 70⁵ " in exponential form and " 1680700000 " in decimal form.

Answer 2

$\mathbb{\red{\huge{HEY\:MATE}}}$

$\boxed{HERE\:IS\:YOUR\:ANSWER}$

$\mathfrak{\green{ANSWER:}}$

There is an mistake in your question.

$\huge{Given\:Question}$

$n = 69^5 + 5×69^4 +10×69^3 + 10×69^2 + 5×59 + 1$

$\huge{Correct\:Question}$

$n = 69^5 + 5×69^4 +10×69^3 + 10×69^2 + 5×69 + 1$

Using the Identity:-

$(a + b) {}^{5} = a {}^{5} + 5a {}^{4}b \: + \: 10a {}^{3} b {}^{2} :\+ \: 10a{}^{2} b{}^{3} \:+\: 5ab{}^{4}\:+ \: b{}^{5}$

Take, a =69 and b=1

Now:-

=》$n = 69^5 + 5×69^4 +10×69^3 + 10×69^2 + 5×69 + 1$

=》$n = (69) {}^{5} + (5×69^4 \times 1 {}^{1}) +(10×69^3 \times 1 {}^{2}) + (10×69^2 \times 1 {}^{3} ) + (5×69×1^4) + (1^5)$

=》$n = (69 + 1) {}^{5}$

=》$n = (70) {}^{5}$

=》$n = 1680700000$

So the value of n is :-

$\huge\boxed{70 {}^{5} \: or \: 1680700000}$