Let Tn be the given series and S_nbe the sum of the given series.∴Tn=2n∴Sn=∑nk−1Tk=∑nk−12k=2∑nk−1k=2[n(n+1)2]=n(n+1)Hence,Sn =n(n+1)
Write the sum of the series : 12−22+32−42+52−62+...+(2n−1)2−(2n)2
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then write the value of k.
Write the sum to n terms of a series whose rth term is :r + 2r.
If ∑nr−1r=55,find ∑nr−1r3
Write the sum of 20 terms of the series: 1+12(1+2)+13(1+2+3)+....