2.42n + 1 + 33n + 1 for all n is divisible by which of the number - 2, 3, 4, 11.

please explain how we can solve such types of other question.

Asked by BHAVYA PREETI | 15th Oct, 2014, 11:03: AM

Expert Answer:

2.4 to the power of 2 n plus 1 end exponent plus 3 to the power of 3 n plus 1 end exponent equals 2.4 to the power of 2 n end exponent.4 plus 3 to the power of 3 n end exponent.3 equals 8.16 to the power of n plus 3.27 to the power of n equals 8.16 to the power of n plus 3. left parenthesis 16 plus 11 right parenthesis to the power of n equals 8.16 to the power of n plus 3. left square bracket 16 to the power of n plus 16 to the power of n minus 1 end exponent.11 n plus to the power of n C subscript 2.16 to the power of n minus 2 end exponent.11 squared plus..................... plus 11 to the power of n right square bracket equals left square bracket 8.16 to the power of n plus 3.16 to the power of n right square bracket plus 3.16 to the power of n minus 1 end exponent.11 n plus 3. to the power of n C subscript 2.16 to the power of n minus 2 end exponent.11 squared plus..................... plus 3.11 to the power of n equals 11.16 to the power of n plus 3.16 to the power of n minus 1 end exponent.11 n plus 3. to the power of n C subscript 2.16 to the power of n minus 2 end exponent.11 squared plus..................... plus 3.11 to the power of n equals 11 open square brackets 16 to the power of n plus 3.16 to the power of n minus 1 end exponent. n plus 3. to the power of n C subscript 2.16 to the power of n minus 2 end exponent.11 plus..................... plus 3.11 to the power of n minus 1 end exponent close square brackets space left square bracket t a k i n g space 11 space c o m m o n space f r o m space a l l space t h e space t e r m s right square bracket  therefore 2.4 to the power of 2 n plus 1 end exponent plus 3 to the power of 3 n plus 1 end exponent space i s space d i v i s i b l e space b y space 11.
Such sums have to be solved by carefully examining the terms, which is to be divided and by what to be divided.

Answered by Prasenjit Paul | 16th Oct, 2014, 10:31: AM

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