Q)sum from r equals 0 to m of left parenthesis negative 1 right parenthesis to the power of r space space space end exponent C presuperscript n subscript r space comma space 0 less than m less than n space i s space e q u a l space t o
left parenthesis A right parenthesis left parenthesis negative 1 right parenthesis to the power of m. C presuperscript n minus 1 end presuperscript subscript m space space space space space left parenthesis B right parenthesis left parenthesis negative 1 right parenthesis to the power of m minus 1 space space end exponent C presuperscript n minus 1 end presuperscript subscript m space space space space space left parenthesis C right parenthesis left parenthesis negative 1 right parenthesis to the power of m. C presuperscript n minus 1 end presuperscript subscript m minus 1 end subscript space space space space left parenthesis D right parenthesis 0

Asked by araima2001 | 4th Apr, 2017, 04:00: AM

Expert Answer:

begin mathsize 16px style Given space that space begin inline style sum from straight r equals 0 to straight m of end style open parentheses negative 1 close parentheses to the power of straight r space straight C presuperscript straight n subscript straight r space space comma space 0 less than straight m less than straight n
As space there space is space condition space given space straight m less than straight n space we space can space not space use space the space formula space for
begin inline style sum from straight r equals 0 to straight n of end style straight C presuperscript straight n subscript straight r equals 2 to the power of straight n
Hence comma space we space will space check space this space by space taking space values space of space straight n space and space straight m space where space straight m less than straight n.
Check space for space any space even space straight n space and space for space odd space straight n.
for space example comma space straight n equals 5 space and space straight m equals 4 space if space we space take space sum space then space it space is space 1.
Checking space with space options space we space get space option space straight A space as space answer.
Also comma space for space straight n equals 6 space and space straight m equals 5
we space get space summation space as space minus 1 space for space the space option space straight A.
The space answer space is space open parentheses negative 1 close parentheses to the power of straight m space. straight C presuperscript straight n minus 1 end presuperscript subscript straight m end style

Answered by Sneha shidid | 4th Apr, 2017, 02:25: PM