"If $\alpha$, $\beta$ are natural numbers such that 100$\alpha$ $-$ 199$\beta$ = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through ($\alpha$, $\beta$) and origin is :"

Question

Accepted Answer

"RHS = $\sum\limits_{r = 0}^{99} {(100 - r)(100 + r)}$

$= {(100)^3} - {{99 \times 100 \times 199} \over 6} = {(100)^3} - (1650)199$

LHS = (100)^$\alpha$ $-$ (199)^$\beta$

So, $\alpha$ = 3, $\beta$ = 1650

Slope = tan$\theta$ = ${\beta \over \alpha }$

$\Rightarrow$ tan$\theta$ = 550"

If $\alpha$, $\beta$ are natural numbers such that
100^$\alpha$ $-$ 199$\beta$ = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through ($\alpha$, $\beta$) and origin is :

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If $\alpha$, $\beta$ are natural numbers such that 100$\alpha$ $-$ 199$\beta$ = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through ($\alpha$, $\beta$) and origin is :

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If $\alpha$, $\beta$ are natural numbers such that
100^$\alpha$ $-$ 199$\beta$ = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through ($\alpha$, $\beta$) and origin is :