InterviewSolution
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The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(2))/(2n) |
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Answer» `UNDERSET(0)OVERSET(1)intx^(n-1)(1-x)^(n)dx` `S = (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"...."+(.^(n)C_(n))/(2n)` `= .^(n)C_(0)underset(0)overset(1)intx^(n-1)+.^(n)C_(1)underset(0)overset(1)intx^(n)dx+"....."+.^(n)C_(n)underset(0)overset(1)intx^(2n-1)dx` `=underset(0)overset(1)int[.^(n)C_(0)x^(n-1)+.^(n)C_(1)x^(n)+"..."+.^(n)C_(n)x^(2n-1)]dx` `= underset(0)overset(1)intx^(n-1)(1+x)^(n)dx` `= underset(1)overset(2)intx^(n)(x-1)^(n-1)dx` |
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