सिर्फ रामानुजन को पता था इसका उत्तर | Ramanujan Infinite Root
Ramanujan’s Nested Radical Problem:
Ramajuan's infinite root. After that I had tried on my own and I got the point.
3=9–√
3=1+8−−−−√
3=1+2⋅4−−−−−−−√
3=1+2⋅16−−√−−−−−−−−−√
3=1+2⋅1+15−−−−−√−−−−−−−−−−−−√
3=1+2⋅1+3⋅5−−−−−−−√−−−−−−−−−−−−−−√
3=1+2⋅1+3⋅25−−√−−−−−−−−−√−−−−−−−−−−−−−−−−√
3=1+2⋅1+3⋅1+24−−−−−√−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−√
3=1+2⋅1+3⋅1+4⋅6−−−−−−−√−−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−−√
3=1+2⋅1+3⋅1+4⋅36−−√−−−−−−−−−√−−−−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−−−−−√
⋮
3=1+2⋅1+3⋅1+4⋅1+⋯−−−−−−√−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−−−−−−−−√
and I also tried
4=16−−√
4=1+15−−−−−√
4=1+2⋅152−−−−−−−−√
4=1+2⋅2254−−−√−−−−−−−−−−√
4=1+2⋅1+2214−−−−−−√−−−−−−−−−−−−−√
4=1+2⋅1+3⋅22112−−−−−−−−√−−−−−−−−−−−−−−−−√
4=1+2⋅1+3⋅48841144−−−−√−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−√
⋮
4=1+2⋅1+3⋅1+4⋅1+⋯−−−−−−√−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−−−−−−−−√
for the value 4. Isn't there a contradiction? I also tried with starting 2=4–√
and it does not work for infinetely times . I sensed that I can do same actions for every number which is greater than and equals to 3
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