A series denotes the sum of terms of a sequentially ordered finite or infinite set of term and summation denotes the process of totaling a series of numbers. The Finite sequences and series have first and last terms, whereas the infinite sequences and series continue indefinitely.

Find sum for the following series Number of terms = 5

Number of terms (n) = 5 Number sequence (k) = 1, 2...5

Sum of Series : ∑k , ∑k2, ∑k3, ∑(k(k+1)), ∑(1/(k(k+1))), ∑(k(k+1)(k+2)), ∑(1/(k(k+1)(k+2))), ∑(2k - 1)

Let us calculate the summation for the given series,

∑k = (5 x (5+1)) / 2 ∑k = 15

∑k^{2} = (5 x (5+1) x ((2 x 5)+1)) / 6
∑k^{2} = 55

∑k^{3} = (5^{2} x (5+1)^{2}) / 4
∑k^{3} = 225

∑(k(k+1)) = (5 x (5+1) x (5+2)) / 3

∑(k(k+1)) = 70

∑(1/(k(k+1))) = 5 / (5+1) ∑(1/(k(k+1))) = 0.8333

∑(k(k+1)(k+2)) = (5 x (5+1) x (5+2) x (5+3)) / 4 ∑(k(k+1)(k+2)) = 420

∑(1/(k(k+1)(k+2))) = 5 x (5+3) / 4 x (5+1) x (5+2) ∑(1/(k(k+1)(k+2))) = 0.23809

∑(2k - 1) = 5^{2}
∑(2k - 1) = 25
Hence, the summation values for the given series are calculated.