Solve n/n+1=(4/5)^100

$$\frac { n } { n + 1 } = ( \frac { 4 } { 5 } ) ^ { 100 }$$

Solve for n

$$n=\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609050603180009858295377285900204390901748568027053919996471339249}\approx 2.037035977 \cdot 10^{-10}$$

Steps for Solving Linear Equation

Variable n cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by n+1.

$$n=\left(n+1\right)\times \left(\frac{4}{5}\right)^{100}$$

Calculate \frac{4}{5} to the power of 100 and get \frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}.

$$n=\left(n+1\right)\times \frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}$$

Use the distributive property to multiply n+1 by \frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}.

$$n=\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}n+\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}$$

Subtract \frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}n from both sides.

$$n-\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}n=\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}$$

Combine n and -\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}n to get \frac{7888609050603180009858295377285900204390901748568027053919996471339249}{7888609052210118054117285652827862296732064351090230047702789306640625}n.

$$\frac{7888609050603180009858295377285900204390901748568027053919996471339249}{7888609052210118054117285652827862296732064351090230047702789306640625}n=\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}$$

Multiply both sides by \frac{7888609052210118054117285652827862296732064351090230047702789306640625}{7888609050603180009858295377285900204390901748568027053919996471339249}, the reciprocal of \frac{7888609050603180009858295377285900204390901748568027053919996471339249}{7888609052210118054117285652827862296732064351090230047702789306640625}.

$$n=\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625}\times \frac{7888609052210118054117285652827862296732064351090230047702789306640625}{7888609050603180009858295377285900204390901748568027053919996471339249}$$

Multiply \frac{1606938044258990275541962092341162602522202993782792835301376}{7888609052210118054117285652827862296732064351090230047702789306640625} and \frac{7888609052210118054117285652827862296732064351090230047702789306640625}{7888609050603180009858295377285900204390901748568027053919996471339249} to get \frac{1606938044258990275541962092341162602522202993782792835301376}{7888609050603180009858295377285900204390901748568027053919996471339249}.

$$n=\frac{1606938044258990275541962092341162602522202993782792835301376}{7888609050603180009858295377285900204390901748568027053919996471339249}$$