Problem 2 with explanation
Problem 2: Find the sum of the Series $\frac{1}{1.3} + \frac{2}{1.3.5} + \frac{3}{1.3.5.7}$ +.... n terms.

Question

Problem 2 with explanation
Problem 2: Find the sum of the Series 1 1 3 + 2 1 3 5 + 3 1 3 5 7 +
n terms

Shruti Tyagi · Accepted Answer

Dear Student,

11 3+21 3 5+31 3 5 7+
n termsthe given series can be written as∑k=1n k1×3×5×
2k+1⇒12∑k=1n 2×k1×3×5×
2k+1 ----multiply and divide by 2⇒12∑k=1n 2×k+1-11×3×5×
2k+1   ---add and subtract 1⇒12∑k=1n 2×k+11×3×5×
2k+1-∑k=1n 11×3×5×
2k+1⇒12∑k=1n 11×3×5×
2k-1-∑k=1n 11×3×5×
2k+1putting values of k=1 to n, we get series as ⇒1211-11×3+11×3-11×3×5+11×3×5-11×3×5×7+
11×3×5×2n-1-11×3×5×2n+1the terms will get cancelled only the first and last terms remain⇒121-11×3×5×2n+1
Regards,

Problem 2 with explanation Problem 2: Find the sum of the Series 1 1.3 + 2 1.3.5 + 3 1.3.5.7 +.... n terms.

Problem 2 with explanation
Problem 2: Find the sum of the Series $\frac{1}{1.3} + \frac{2}{1.3.5} + \frac{3}{1.3.5.7}$ +.... n terms.