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JEE Class main Answered

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Asked by sanjaysingh.srct | 24 Jul, 2019, 08:19: AM
answered-by-expert Expert Answer
S subscript k left parenthesis 1 right parenthesis equals 1 to the power of k comma space S subscript k left parenthesis 2 right parenthesis equals 1 to the power of k plus 2 to the power of k comma...... space S subscript k left parenthesis n minus 1 right parenthesis equals 1 to the power of k plus 2 to the power of k plus... plus left parenthesis n minus 1 right parenthesis to the power of k space a n d space
S subscript k plus 1 end subscript left parenthesis n right parenthesis equals 1 to the power of k plus 1 end exponent plus 2 to the power of k plus 1 end exponent plus.. plus n to the power of k plus 1 end exponent
equals 1 to the power of k plus 2 times 2 to the power of k plus 3 times 3 to the power of k plus... plus n times n to the power of k
equals 1 to the power of k plus left parenthesis 2 to the power of k plus 2 to the power of k right parenthesis plus left parenthesis 3 to the power of k plus 3 to the power of k plus 3 to the power of k right parenthesis plus... plus left parenthesis n to the power of k plus n to the power of k plus.. n t i m e s right parenthesis
T h e r e f o r e comma

S subscript k plus 1 end subscript left parenthesis n right parenthesis plus S subscript k left parenthesis n minus 1 right parenthesis plus S subscript k left parenthesis n minus 2 right parenthesis plus... plus S subscript k left parenthesis 2 right parenthesis plus S subscript k left parenthesis 1 right parenthesis
equals open square brackets 1 to the power of k plus left parenthesis 2 to the power of k plus 2 to the power of k right parenthesis plus left parenthesis 3 to the power of k plus 3 to the power of k plus 3 to the power of k right parenthesis plus... plus left parenthesis n to the power of k plus n to the power of k plus.. n t i m e s right parenthesis close square brackets plus 1 to the power of k plus 2 to the power of k plus... plus left parenthesis n minus 1 right parenthesis to the power of k plus.... plus 1 to the power of k plus 2 to the power of k plus 1 to the power of k
equals n times 1 to the power of k plus n times 2 to the power of k plus... plus n times n to the power of k
equals n left parenthesis 1 to the power of k plus 2 to the power of k plus... plus n to the power of k right parenthesis
equals n S subscript k left parenthesis n right parenthesis
Answered by Renu Varma | 24 Jul, 2019, 10:26: AM
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