Question

C= 1.4 + 2.5 + 3.6 +...... + 99.102

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Answer 1

\(C=1.4+2\left(4+1\right)+3\left(4+2\right)+...+99\left(4+98\right)\)

\(\Leftrightarrow C=1.4+2.4+1.2+3.4+2.3+...+99.4+98.99\)

\(C=\left(1.4+2.4+3.4+....+99.4\right)+\left(1.2+2.3+3.4+..98.99\right)\)

\(C=4\left(1+2+3+...+99\right)+\dfrac{1.2.3+2.3.3+3.4.3+...+98.99.3}{3}\)

\(C=\dfrac{4.\left(1+99\right).99}{2}+\dfrac{1.2.3+2.3\left(4-1\right)+...+98.99\left(100-97\right)}{3}\)

\(C=\dfrac{4.\left(1+99\right).99}{2}+\dfrac{1.2.3+2.3.4-1.2.3...+98.99.100-97.98.99}{3}\)

\(C=\dfrac{4.\left(1+99\right).99}{2}+\dfrac{98.99.100}{3}\)

\(C=19800+107800=127600\)