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Euclid Sample Paper 1 · Q10

Paper 1Sequences & series

A sequence (xn)(x_n) is defined by

x1=2,xn+1=xn1+xn.x_1=2,\qquad x_{n+1}=\frac{x_n}{1+x_n}.

What is the value of

∑n=120xnxn+1?\sum_{n=1}^{20}x_nx_{n+1}?
A4041\frac{40}{41}
B6041\frac{60}{41}
C8041\frac{80}{41}
D22
E4021\frac{40}{21}
F8241\frac{82}{41}

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