Question

B= 7/1x4+7/4x7+7/7x10+......+7/46x49

Answer 1

\(B=\dfrac{7}{1\times4}+\dfrac{7}{4\times7}+...+\dfrac{7}{46\times49}\\ =7\times\left(\dfrac{1}{1\times4}+\dfrac{1}{4\times7}+...+\dfrac{1}{46\times49}\right)\\ =\dfrac{7}{3}\times\left(\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+...+\dfrac{3}{46\times49}\right)\\ =\dfrac{7}{3}\times\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{46}-\dfrac{1}{49}\right)\\ =\dfrac{7}{3}\times\left(1-\dfrac{1}{49}\right)\\ =\dfrac{7}{3}\times\dfrac{48}{49}\\ =\dfrac{16}{7}\)