help qs 6 induction

[candid magnet]

You can prove this by induction

For the induction, you can use the fact that your sequence follows the rule $u_{n+1} = u_n + (-1)^{n+1}/n$

[hardy stream]

Twenty

[mystic walrus]

I don’t know what to do from there

[rustic pelican]

Where?

n+1?

[rustic pelican]

Change the exponent n+1 on (-1) to n and the n to n+1

[rustic pelican]

Hint: discuss whether n is even or not

[candid magnet]

right, thanks

[candid magnet]

$u_{n+1} = u_n + (-1)^{n}/(n+1)$

[hardy stream]

Twenty

[candid magnet]

Recall that induction goes as:

• Case n=0 : you have to check that u_0 is positive
• Take any integer n and assume that u_n>0 and prove from this that u_{n+1} is positive