plz gv me some other interesting maths exhibition projects related to 11 and 12 th grade

Asked by archana | 5th Dec, 2015, 10:45: PM

Expert Answer:

U sin g space b i n o m i a l space T h e o r e m comma space w e space c a n space f i n d space t h e space v a l u e space o f space 2 to the power of 1000. W e space n e e d space t o space c o d e space a space p r o g r a m space i n space t h e space c o m p u t e r space t o space f i n d space t h e space v a l u e space o f space 2 to the power of 1000.  2 space c a n space b e space w r i t t e n space a s comma space 2 equals 1 plus 1 T a k i n g space t h e space p o w e r space t o space 1000 space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma 2 to the power of 1000 equals open parentheses 1 plus 1 close parentheses to the power of 1000 B i n o m i a l space T h e o r e m space s t a t e s space t h a t comma I f space x space a n d space a space a r e space r e a l space n u m b e r s comma space t h e n space f o r space a l l space n element of N comma open parentheses x plus a close parentheses to the power of n equals C presuperscript n subscript 0 x to the power of n a to the power of 0 plus C presuperscript n subscript 1 x to the power of n minus 1 end exponent a to the power of 1 plus C presuperscript n subscript 2 x to the power of n minus 2 end exponent a squared plus C presuperscript n subscript 3 x to the power of n minus 3 end exponent a cubed plus... plus C presuperscript n subscript r x to the power of n minus r end exponent a to the power of r plus... plus C presuperscript n subscript n minus 1 end subscript x to the power of 1 a to the power of n minus 1 end exponent plus C presuperscript n subscript n x to the power of 0 a to the power of n  T h u s comma space a p p l y i n g space b i n o m i a l space t o space t h e space e x p r e s s i o n comma space comma space w e space h a v e comma open parentheses 1 plus 1 close parentheses to the power of 1000 equals C presuperscript 1000 subscript 0 cross times 1 to the power of 10000 cross times 1 to the power of 0 plus C presuperscript 1000 subscript 1 cross times 1 to the power of 999 cross times 1 to the power of 1 plus C presuperscript 1000 subscript 2 cross times 1 to the power of 998 cross times 1 squared plus C presuperscript 1000 subscript 3 cross times 1 to the power of 997 cross times 1 cubed space space space space space space space space space space space space space space space space space space space space space plus... plus C presuperscript 1000 subscript r cross times 1 to the power of n minus r end exponent cross times 1 to the power of r plus... plus C presuperscript 1000 subscript 999 cross times 1 to the power of 1 cross times 1 to the power of 999 plus C presuperscript 1000 subscript 1000 cross times 1 to the power of 0 cross times 1 to the power of 1000 space space space space space space space space space space space space space space space space equals C presuperscript 1000 subscript 0 plus C presuperscript 1000 subscript 1 plus C presuperscript 1000 subscript 2 plus C presuperscript 1000 subscript 3 space plus... plus C presuperscript 1000 subscript r plus... plus C presuperscript 1000 subscript 999 plus 1 N o w space a d d i n g space a l l space t h e space v a l u e s space w e space g e t space 2 to the power of 1000

Answered by Vimala Ramamurthy | 7th Dec, 2015, 10:37: AM

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