T20 fever!

Algebra Level 3

Imagine a T20 match, where the batsmen score with a rate of $f(x)= x^2+1$ , where $x$ is the $x^{\text {th}}$ over of the match. What are the total runs scored in the innings?

Details and assumptions

Disregard the rules of cricket.

A T20 match has 20 overs.

The answer is 2890.

1 solution

Rishabh Jain
Mar 16, 2016

We have to find $\mathbf S=f(1)+f(2)+f(3)+\cdots f(20)$ $\large \begin{aligned} \therefore\mathbf S&=\displaystyle\sum_{x=1}^{20}( x^2)+20\\&=\dfrac{20(21)(41)}{6}+20\\&=\boxed{2890}\end{aligned}$

$\mathbf{NOTE:-}\\ (1)~\large\color{#302B94}{\displaystyle\sum n^2=\dfrac{n(n+1)(2n+1)}{6}}$

$(2)$ For this to be true the team has to score $144.5$ runs per over or $24.083\cdots$ runs per ball.. Lol ;-)..

Hell, if India plays like that...we'd be UNBEATABLE !!!

A Former Brilliant Member - 5 years, 3 months ago

Very true.... But its hypothetical you know... :-)

Rishabh Jain - 5 years, 3 months ago

Yep...unless we play against a team that bowls 4-5 no-balls before a legit ball, and the batsman is the Yuvraj who hit 6 sixes! :P

A Former Brilliant Member - 5 years, 3 months ago

YOU POSTED A SOLUTION ALREADY? DUDE RELAX!!

Mehul Arora - 5 years, 3 months ago

LOL! xD (Ninjaed :P )

Nihar Mahajan - 5 years, 3 months ago

Exactly. Ninja-ed.

Mehul Arora - 5 years, 3 months ago

So you were writing a solution too?? Sorry for that !! :-)

Rishabh Jain - 5 years, 3 months ago

Maintaining your brilliant status should be hell difficult for you, 'coz you get a single up-vote in every $t$ seconds, where $t = lim_{x \rightarrow \infty}\dfrac{1}{x}$

Harsh Shrivastava - 5 years, 3 months ago

@Harsh Shrivastava – Hahahahah yes :P

Mehul Arora - 5 years, 3 months ago

What do you mean you were writing it TOO? You've to let others write solutions :P

Slow down your pace :P

Mehul Arora - 5 years, 3 months ago

T20 fever!

The answer is 2890.

1 solution

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