How to know where we have to use (2n-1) And where to use (2n+1) in wave optics for minima in ydse

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Q. Let

u_{1}

= 1,

u_{2}

= 1 and

u_{n + 2} + u_{n} f o r n \geq 1

.
Use mathematical induction to show that

u_{n} = \frac{1}{\sqrt{(5)}} [{(\frac{1 + \sqrt{5}}{2})}^{n} - {(\frac{1 - \sqrt{5}}{2})}^{n}]

for all

n \geq 1

Q. Use the principle of mathematical induction to show that :

2 + 2^{2} + . . . . . + 2^{n} = 2^{n + 1} - 2

for every natural number

n .

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