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Asked by sarveshvibrantacademy | 02 May, 2019, 00:07: AM
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left parenthesis d right parenthesis limit as n rightwards arrow infinity of space sum from k equals 0 to n of fraction numerator 1 over denominator large C subscript k superscript n end fraction F o r space k element of open square brackets 2 comma n minus 2 close square brackets comma space w e space h a v e large C subscript k superscript n greater or equal than fraction numerator n left parenthesis n minus 1 right parenthesis over denominator 2 end fraction A n d space w e space k n o w space t h a t sum from k equals 0 to n of fraction numerator 1 over denominator large C subscript k superscript n end fraction equals 1 plus 1 over n plus sum from k equals 2 to n minus 2 of fraction numerator 1 over denominator large C subscript k superscript n end fraction plus 1 over n plus 1 rightwards double arrow space 1 plus 1 over n plus 1 over n plus 1 less or equal than 1 plus 1 over n plus sum from k equals 2 to n minus 2 of fraction numerator 1 over denominator large C subscript k superscript n end fraction plus 1 over n plus 1 less or equal than 1 plus 1 over n plus sum from k equals 2 to n minus 2 of fraction numerator n left parenthesis n minus 1 right parenthesis over denominator 2 end fraction plus 1 over n plus 1 rightwards double arrow 2 plus 2 over n less or equal than sum from k equals 0 to n of fraction numerator 1 over denominator large C subscript k superscript n end fraction less or equal than 2 plus 2 over n plus left parenthesis n minus 3 right parenthesis. fraction numerator 2 over denominator n left parenthesis n minus 1 right parenthesis end fraction N o w comma space 2 plus 2 over n rightwards arrow 2 space a s space n rightwards arrow infinity A l s o comma space 2 plus 2 over n plus left parenthesis n minus 3 right parenthesis. fraction numerator 2 over denominator n left parenthesis n minus 1 right parenthesis end fraction rightwards arrow 2 space a s space space n rightwards arrow infinity T h u s comma space a l l space t h e space t e r s space c o n v e r g e space t o space 2. H e n c e comma space sum from k equals 0 to n of fraction numerator 1 over denominator large C subscript k superscript n end fraction space t e n d s space t o space 2 space a s space n rightwards arrow infinity
Answered by Renu Varma | 03 May, 2019, 12:32: PM

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