# What will be the value of 1% of 2 + 2% of 3 + 3% of 4 +...............+ 99% of 100 = ?

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Below given are two formulae for long summation.
1) 1 + 2 + 3 + 4 +......................... +n = n(n+1) / 2
2) 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + ............................+ n ^ 2 = 1 / 6 n (n+1) (2n+1)
What will be the value of 1% of 2 + 2% of 3 + 3% of 4 +...............+ 99% of 100 = ?

posted Feb 5, 2015

+1 vote

1% of 2 + 2% of 3 + 3% of 4 + ....... 99% of 100
= (1% of 1 + 2% of 2 + 3% of 3 + ....... 99% of 99) + (1% of 1 + 2% of 1 + 3% of 1 + ...... 99% of 1)
= [(1^2 + 2^2 + ..... + 99^2)/100] + [(1+2+3+..... + 99)*1/100]
= [1/6*(99)(100)(199)/100] + [1/2*(99)(100)(1)/100]
= 3333

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