If n is odd, then an + bn is divisible by (a + b) and an− bn is divisible by (a − b). If n is even, then an− bn is divisible by (a − b) and (a + b) .

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If n is odd, then an + bn is divisible by (a + b) and an− bn is divisible by (a − b). If n is even, then an− bn is divisible by (a − b) and (a + b) .

If n is odd, then aⁿ+ bⁿ is divisible by (a + b) and aⁿ− bⁿ is divisible by (a − b). If n is even, then aⁿ− bⁿ is divisible by (a − b) and (a + b) .The remainder when 1²⁰¹¹+2²⁰¹¹+3²⁰¹¹+…….+2010²⁰¹¹ is divided by 2011 will be

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

1²⁰¹¹ + 2²⁰¹¹ + 3²⁰¹¹ +...... +2010²⁰¹¹

= (1²⁰¹¹ + 2010²⁰¹¹) + (2²⁰¹¹ + 2009²⁰¹¹) + (3²⁰¹¹ + 2008²⁰¹¹) ...... (1011²⁰¹¹ + 1000²⁰¹¹)

These terms are of the form aⁿ + bⁿ, so they will be divided by a + b, as n = 2011 which is an odd number.

Clearly, in the series a + b = 2011. Hence, the remainder is 0.

If n is odd, then an + bn is divisible by (a + b) and an− bn is divisible by (a − b). If n is even, then an− bn is divisible by (a − b) and (a + b) .

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