Write out the sum sigmank 1 k28 sigmank 1 k28 Type the fi

Write out the sum. sigma^n_k = 1 k^2/8 sigma^n_k = 1 k^2/8 = (Type the first, second, and final terms. Type fully reduced fractions where appropriate.)

Solution

for first term plug k=1 in the given equation

1st term = 1^2/8 = 1/8

2nd term = 2^2/8 = 4/8

final term = n^2/8

sum of all the terms in the series is = 1^2/8 +2^2/8 +3^2/8 +..................................+n^2/8

= 1/8 [ 1^2 +2^2 +3^2 +.................+ n^2 ]

=1/8 [ n(n+1)(2n+1)/6]

= n(n+1)(2n+1)/48