15th 

Asked by lovemaan5500 | 12th Jul, 2018, 10:09: PM

Expert Answer:

begin mathsize 16px style begin inline style sum from straight r equals 0 to straight n of 3 to the power of straight r cross times straight C presuperscript straight n subscript straight r
Using space binomial space expansion
sum from straight r equals 0 to straight n of 3 to the power of straight r cross times straight C presuperscript straight n subscript straight r equals sum from straight r equals 0 to straight n of straight C presuperscript straight n subscript straight r cross times straight a to the power of straight n minus straight r end exponent cross times straight b to the power of straight r
Comparing space both space sides comma
straight a equals 1 space and space straight b equals 3
sum from straight r equals 0 to straight n of straight C presuperscript straight n subscript straight r cross times 1 to the power of straight n minus straight r end exponent cross times 3 to the power of straight r space which space is space sum from straight r equals 0 to straight n of 3 to the power of straight r cross times straight C presuperscript straight n subscript straight r
Put space the space same space values space in space left parenthesis straight a plus straight b right parenthesis to the power of straight n equals left parenthesis 1 plus 3 right parenthesis to the power of straight n equals 4 to the power of straight n
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Answered by Sneha shidid | 13th Jul, 2018, 11:41: AM