1/1.3 +1/3.5 + 1/5.7 +1/7.9 ......sum to n terms Share with your friends Share 4 Manbar Singh answered this We have,an = 1nth term of 1,3,5,..... × nth term of 3,5,7,......an=11+n-12×3+n-12an=12n-12n+1Let 12n-12n+1 = A2n-1 + B2n+1⇒12n-12n+1 = 2An + A + 2Bn - B2n-12n+1⇒1 = 2A + 2Bn + A - B .......1Comparing the coefficients of n both sides, we get2A + 2B = 0⇒A + B = 0 .......2Comparing the constant on both sides, we getA - B = 1 ........3Adding 2 and 3, we get2A = 1 ⇒A = 12Now, from 1, we get B = -12Now, 12n-12n+1 = 1212n-1 - 12n+1⇒ak = 1212k-1 - 12k+1Now, a1 = 121 - 13a2 = 1213 - 15a3 = 1215 - 17continuing in the same manner, we getan-1 = 1212n-3 - 12n-1an = 1212n-1 - 12n+1Now, adding columnwise, we getSn = ∑k=1nak = 121 - 12n+1 = 122n+1-12n+1 = n2n+1 7 View Full Answer
