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Question Number 133653 by greg_ed last updated on 23/Feb/21

hi, everybody!

how to prove that π is an irrational number ? ? ?

Answered by Dwaipayan Shikari last updated on 23/Feb/21

1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \frac{1}{11} + \dots = \frac{π}{4}

A s I t i s a n I n f i n t e s e r i e s s o i t c a n n e v e r b e r a t i o n a l

O t h e r s e r i e s

1 + \frac{1}{2^{4}} + \frac{1}{3^{4}} + \dots = \frac{π^{4}}{90}

1 + \frac{1}{2} {(\frac{1}{2.1!})}^{2} + \frac{1}{3} {(\frac{1.3}{2^{2} . 2!})}^{2} + \frac{1}{4} {(\frac{1.3.5}{2^{3} . 3!})}^{2} + \dots = \frac{4}{π}